Russia and Egypt have urged caution over suggestions from the UK and US that a Russian airliner that crashed in Sinai on Saturday, killing 224 people, may have been bombed.
The Russian foreign ministry said it was "shocking" that Britain had not shared the evidence.
A number of countries have restricted travel to the Sharm el-Sheikh resort, from where the plane had departed.
Militants linked to Islamic State have claimed they brought the plane down.
The Metrojet Airbus 321, bound for St Petersburg and carrying mostly Russian citizens, crashed in Egypt's Sinai desert just 23 minutes after take-off from Sharm el-Sheikh.
UK Prime Minister David Cameron said "intelligence and information" available to his government suggested that a bomb was "more likely than not" to have brought down the airliner.
He and the Russian President Vladimir Putin spoke by phone on Thursday afternoon.
Later on Thursday, the UK government announced it would start to repatriate thousands of Britons who were stranded after the UK suspended all flights to and from the Red Sea resort.
Passengers will only be allowed on board with hand baggage while hold luggage will be transported separately, a spokesman said.
Egyptian President Abdul Fattah al-Sisi - in Downing St for talks on his first official visit to the UK - earlier said that Egypt was completely ready to co-operate "with all our friends" over security measures at Sharm el-Sheikh airport.
The Egyptian leader said British experts examined procedures at the airport 10 months ago, and were happy with what they found.
Mr Cameron said that the UK and Egypt were "working intensively together". His role was to "act in the right way" to keep British citizens safe and secure, he said.
In the US, the White House said that "some information has been learned" that supports Britain's suspicions that a bomb was responsible for the plane crash.
White House spokesman Josh Earnest said that nothing can be ruled out, "including terrorist involvement".
He said that a review of safety for commercial flights bound for the US is taking place and an announcement will soon be made by the Department of Homeland Security.
The IS affiliate Sinai Province, which emerged in 2011, reiterated its claim of responsibility on Wednesday.
"We brought it down by God's help, but we are under no obligation to reveal the mechanism we used," an audio statement circulating on social media said.
Egypt's Tourism Minister Hisham Zaazou described the British decision on Wednesday to cancel all flights as "unjustified".
Egypt is leading the investigation into the air disaster, with the help of Russian and other foreign experts.
They will examine the wreckage for traces of explosives, but would not reach their first conclusions for a few months, said Alexander Neradko, head of Russia's aviation agency.
In other developments:
- German airline Lufthansa says its subsidiaries Edelweiss and Eurowings are halting flights to Sharm el-Sheikh as a "precautionary" measure and will arrange return flights
- Belgian airline Jetairfly postponed its Thursday flight from Brussels to the Egyptian resort for 24 hours while it analysed the security situation
- Both France and the Netherlands are advising their citizens against travel to and from Sharm el-Sheikh airport
- Ireland and the UK announced the suspension of all flights to the resort on Wednesday, but the UK later said it would start to repatriate Britons on Friday
Lyse Doucet, BBC News, Cairo
The timing of Britain's statement on the air crash could not have been worse, just as President Sisi was arriving in London for his first official visit.
A senior official in his delegation told me this morning they were not told in advance. He said this would be one of the most important topics in today's meeting between the two leaders and would have an impact on other issues. We won't be as receptive, is how he put it.
Egyptian officials say they had responded to every British request for extra security at Sharm el-Sheik airport including additional troops in and around the airport.
This is a hugely embarrassing moment for the Egyptian authorities but, if it is proven that a bomb was on board the plane, they also face troubling questions about their ability to maintain security in the midst of significant threats.
Metrojet, also known as Kogalymavia, earlier this week blamed "external influence" for the crash, but the head of Russia's aviation agency said such talk was premature.
On Thursday, the airline suspended all flights of Airbus A321 jets in its fleet.
The Russian press has been playing down the idea that Islamist militants might be targeting Russia over its aerial bombing campaign in Syria.
A senior member of Russia's upper house of parliament, Konstantin Kosachev, was quoted as saying that Britain's move was "politically motivated by its opposition to Russia's actions in Syria".
Also on Thursday, the first funeral for a victim of the crash was held in Russia.
Nina Lushchenko, a 60-year-old school employee, was buried in Veliky Novgorod, south of St Petersburg.
At the scene: Sarah Rainsford, BBC News, St Petersburg
Anxious for information, Olga Ovechkina and other relatives now come to a hotel near the airport each day.
It has become the headquarters for an emergency response team. Raw-eyed relatives wander the lobby here or sit quietly and cry.
Dozens of psychologists are on hand to offer comfort, themselves clearly drained by the experience.
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