Thank you for following today's live coverage of the investigation into the 13 November Paris attacks and the continuing terror alert in Belgium. We will resume our live coverage early on Tuesday morning UK time. In the meantime you can follow all the developments on our homepage.
- Brussels enters third day of lockdown on highest level of alert
- Jets from a French aircraft carrier in the eastern Mediterranean have begun missions against Islamic State
- Belgian police arrest 21 people in raids after Paris attacks
- Suspected Paris gunman Salah Abdeslam still at large
- UK Prime Minister David Cameron visits Bataclan concert hall with President Hollande
- All times GMT
The BBC's World Have Your Say programme has been speaking to Brussels residents to get their views on the shutdown. Stephane, a cafe-owner in central Brussels, said it had become "a ghost city".
"It's an overreaction, it only creates mass hysteria," he said. See more here.
"A belt that may resemble an explosive belt" has been found in the southern Paris suburb of Montrouge, AFP news agency is reporting.
A police source told the agency that the object was found in a dustbin. A source close to the inquiry said telephone data placed Salah Abdeslam, a key suspect in the attacks who is still on the run, in the Montrouge area on the night of the attacks.
Many countries have had a more visible security presence after the Paris attacks. Here an Italian soldier patrols in Rome's Termini train station.
Although many visitors are steering clear of Brussels, one old-timer in the city told the BBC's Gavin Lee she was undeterred by the lockdown:
One cafe has opened, one where it's usually hard to get a seat. Today there is one customer, a lady eating a late breakfast. Sylvia is 75, and has been here every day for twenty years. “I am not afraid. We have a lot of security measures, I don’t think the terrorists will attack now, and I’ll be here tomorrow. It’s my way of showing resistance."
AP has more on the explosive belt reportedly found in the Paris suburb of Montrouge.
It quotes a police official as saying it was found by a street cleaner on Monday in a pile of rubble.
Police are currently analysing the belt to see if it may have been used in the 13 November attacks that killed 130 people, the official said.
The AP agency quote French police as saying that an explosive belt without a detonator has been found in the southern Parisian suburb of Montrouge.
The Belgian government and the Belgian people are facing a very difficult situation and I want to thank the people for their understanding - I also want to thank our security services, they are working very hard.
Mr Michel says the Brussels metro system will also re-open "gradually" from Wednesday.
We have today decided to maintain the alert level at the maximum level of 4, the situation is the same with a serious and imminent threat for Brussels. The rest of the country remains at level 3.
Belgian Prime Minister Charles Michel announces at a press conference that the capital Brussels will remain at the highest alert level until next Monday.
Schools will re-open from this Wednesday, he said.
The BBC's Gavin Lee has been speaking to the few people out and about in Brussels.
Today I walked through the Royal Gallery of St Hubert. I counted on one hand the number of shoppers. This place is an essential tourist stop, with Belgian’s finest chocolates on display. Only one has opened, with armed soldiers outside, and it has barely any customers. Two Danish tourists select some macaroons, looking over their shoulders as I enter. "We were told by the hotel manager not to come here, but we thought we’d take a chance. Buy presents for the family and leave quickly." Eva, behind the counter, says her boss told her she could have the day off if she was afraid. She says: "I feel I'd be letting myself down if I didn’t come in, even if no-one comes in to be served."
The Belgian prosecutor says one of suspects detained in a counter-terror operation has been charged with involvement in the Paris attacks.
Fifteen of the 16 people who were detained in operations on Sunday night have since been released, the prosecutor's office said.
Belgian officials are expected to announce shortly whether they will maintain the current high alert in Brussels for another day.
At least one local official - the mayor of Vilvoorde, a municipality bordering Brussels - has said schools in his district will remain closed tomorrow, regardless of what Brussels authorities decide.
Media in Belgium's neighbouring countries have been pondering the repercussions of the alert in Brussels.
Belgian newspaper La Libre says Brussels now "lives in fear" as "a target". It asks if this is the aim of the terrorists: "Has 'the work been done' as we feared, restricting our movements, taking away our leisure, and imposing a kind of curfew?"
Dutch newspaper NRC highlights tough criticism of Belgium's failure to "clamp down" on violent Islamism.
German conservative paper Die Welt says that "fear of terror will be the city's constant companion in the coming days", adding: "There is little evidence that the major night-time police deployment will restore the confidence of the people of Brussels that they are safe once again."
French left-leaning L'Humanite fears that rising security or counter-terrorism measures might lead to increased violence from both sides of the political spectrum.
BBC Monitoring has produced a more detailed roundup of the press reaction.
A selection of images from the third day of the lockdown in Brussels, where soldiers accompanied police on streets lacking their characteristic bustle.
Belgian daily Le Soir has been analysing the impact of the Brussels lockdown.
"The lockdown paralyses Brussels and gradually the whole country in a climate of anxiety," it says. "The 'lockdown' of a city for a long period as a precaution against a terrorist threat is unprecedented, not only in Belgium."
The paper also accuses the authorities of creating "horrible confusion" by way of contradictory statements on the situation.
Mourners gather to bury two victims of the Paris attacks, Anna and Marion Petard-Lieffrig, outside the Saint Louis Cathedral in Blois, central France, on Monday.Anna, 26, and her sister Marion, 30, were killed in the Le Petit Cambodge restaurant, the AFP news agency reported.
French President Hollande is meeting four world leaders in as many days, to discuss topics ranging from the Syrian conflict to intelligence-sharing between European countries.
This morning he met with UK Prime Minister David Cameron to discuss co-operation in the fight against the so-called Islamic State. He next flies to Washington to see US President Barack Obama, before returning to Paris for a meeting with German Chancellor Angela Merkel on Wednesday.
And on Thursday, he is off to Moscow for talks with Russian President Vladimir Putin.
Read Lucy Williamson's full report on French diplomacy following the Paris attacks.
The emergence of violent jihadism in Belgium is certainly troubling - but the factors behind it are complex, and not entirely confined to Belgium, says Bart Cammaerts, of the London School of Economics' Europp blog.
Ultimately, while attention is now on Belgium and its failures in dealing with the creeping radicalisation of some of its young Muslim citizens, the reasons for this radicalisation are relevant to many other European countries and cannot be reduced to any one factor alone. Above all, European countries must show the courage to reflect internally on how they treat their own Muslim citizens in their educational systems, their job and housing markets, and in everyday life.
French warplanes have launched their first mission over Syria and Iraq from the aircraft carrier, Charles de Gaulle. The ship in the eastern Mediterranean carries enough planes to more than double France's ability to strike the Islamic State group.
President Hollande has promised to intensify operations against the militants in response to the Paris attacks.
French aircraft have been flying missions over Syria from bases in Jordan and the United Arab Emirates since September.
Many public spaces in Western cities have been redesigned to reduce the risk and possible impact of bombs. But some of these measures have also made it harder to take cover during a gun attack, according to the New Statesman's City Metric blog.
While aiding the early detection of suspicious items and behaviour, there’s a nasty rub. In a different attack context, these same carefully crafted, uncluttered and open spaces can increase vulnerability. Passengers who are unable to flee the immediate vicinity, for example, find themselves sitting ducks with nowhere to hide from determined gunman bent on killing as many people as possible before the cavalry arrives.
The BBC's Gavin Lee speaks to tourists in Brussels:
Signs that the attacks in Paris have impacted France's service sector have emerged in the latest survey by Markit.
The firm said a rapid fall-off in trade was behind its index falling from 52.7 in October to 51.3 in November.
"We think the key reason for the slowing in services growth is due to the attacks," Chris Williamson, Markit's chief economist said.
"But history does tell us that these events tend to have a very short-lived impact," added Mr Williamson.Read the full report.
How is the lockdown affecting those living in Brussels?
Schools - Schools and universities in Brussels remained closed on Monday.
Transport - Transport authorities in Brussels suspended the city's Metro underground transport system and some bus routes.
Passengers faced tightened security checks for Thalys and TGV high-speed trains from Brussels Gare du Midi train station.
Work places - Many offices have remained open for a normal working day, but some have advised employees to stay at home.
Tourism - Twitter users reported on Monday that the city's main tourist attractions, such as the Grand Place central square, were unusually quiet.
The Brussels airport is open and all flights are running as normal, but there are increased security measures in place. Read more here.
The French finance minister, Michel Sapin, has announced a series of initiatives to improve the tracking of terrorism financing, Le Monde newspaper reports.
The measures include better supervision of prepaid bank cards, which the ministry believes played an important role in the preparation of the 13 November attacks.
The new measures will make it harder for card users to remain anonymous. Currently, prepaid cards can be recharged without identity checks, so long as they do not exceed 2,500 euros over one year, according to the AFP news agency.
"There are new means of payment which have been created which should be on our radar," Bruno Dalles, head of the finance ministry's Tracfin intelligence unit, told AFP.
During Sunday night's operations in Brussels, Belgians helped police to drown out any leaking of operational details on Twitter.
Using the hashtag #BrusselsLockdown, which was earlier used to tweet updates on the operation, Twitter users posted pictures and videos of cats.
Now federal police has thanked them with a tweet: "To all the cats who helped us last night: help yourselves! #BrusselsLockdown"Read the full story here
France has stepped up security in schools as it continues to enforce its anti-terrorism system, Vigipirate.
Measures include bag checks, a ban on school trips, and mandatory fire and evacuation drills.
Special "smoking areas" are also being introduced within schools to prevent students from leaving the premises.
Read more here.
The Belgian prosecutor's statement mentions that a BMW that evaded a police check on Sunday night has since been traced - and is not linked to the counter-terror operation.
Reports of the BMW's escape prompted speculation that Paris attacks suspect Salah Abdeslam had fled Belgium for Germany. The vehicle sped away from police in the Liege region, which borders Germany.
The Davis Cup final between Belgium and Great Britain will go ahead despite the terror threats affecting Brussels, according to the Flemish Tennis Federation.
The final is due to start in Ghent on Friday, 55km (35 miles) away from the Belgian capital, which is currently under the country's highest security alert.
"It's definitely going ahead," a spokeswoman for the Flemish Tennis Federation told the Reuters news agency.
She added that the public would be advised on Tuesday about security measures for the final, which will be played from Friday to Sunday.
A further five people have been arrested in Belgium, a spokesperson for the Belgian prosecutor said.
A total of 21 people have now been arrested in counter-terror operations since Sunday.
The latest statement from the prosecutor said a further five houses had been searched in the Brussels region, and two in the Liege area.
A sum of €26,000 (£18,300;$27,600) was reportedly seized during one of the searches.
Fouad Belkacem,ringleader of the Sharia4Belgium group, will not be allowed any contact with fellow prisoners in Antwerp, the Gazet van Antwerpen reported.Prison authorities fear that Belkacem could radicalise other prisoners amid heightened tensions in the prison after the attacks in Paris.
Following the attacks, special safety measures for guarding Belkacem were put in place.
"He is not allowed to go to worship and he may not go walking or relaxing," a member of Belkacem's council advocate Nabil Riffi told Gazet van Antwerpen
Belkacem was sentenced to 12 years in prison in February, along with 45 other members of the Sharia4Belgium group.
The judge said he was "responsible for the radicalisation of young men to prepare them for Salafist combat, which has at its core no place for democratic values"..
Brussels tourist attraction, the Atomium, has announced that its doors will remain closed today, dashing hopes that it may open to visitors.
French Defence Minister Jean-Yves Le Drian says the flagship aircraft carrier, Charles de Gaulle, which is already in the waters off the Syrian coast, should be ready to take part in strikes against the IS group, France's Europe 1 radio reports.
France hopes the involvement of the warship will shorten the time it takes for French jets to carry out air strikes. The aircraft carrier can hold up to 40 aircraft and support 100 flights a day. It has already served as a base for French jets in the Gulf which took part in strikes against IS earlier this year.
Nato says its headquarters in Brussels are open, but some staff have been asked to work from home and external visits have been cancelled, the Reuters news agency reports.
The alliance raised its alert level after the Paris attacks of 13 November.
EU institutions are also open with soldiers patrolling outside, Reuters reports.