A terror attack near a London mosque is "every bit as sickening" as others in recent weeks, Theresa May says.
A man drove a van into worshippers close to Muslim Welfare House in Finsbury Park as they were gathered to help an elderly man who had collapsed.
He later died, but it is not clear if this was a result of the attack. Nine other people were taken to hospital.
A 47-year-old man was held on suspicion of attempted murder and later further arrested over alleged terror offences.
Scotland Yard said he was being held on suspicion of the commission, preparation or instigation of terrorism including murder and attempted murder.
Searches are also being carried out at an address in the Cardiff area.
Met Police Commissioner Cressida Dick said the incident in north London was "quite clearly an attack on Muslims", and the community would now see more police, including armed officers, in the area, "particularly around religious establishments".
It is the fourth terror attack in the UK in three months, after incidents in Westminster, Manchester and on London Bridge.
Police said all the victims of the attack shortly after midnight were Muslim and many were believed to have just left evening prayers after breaking the Ramadan fast.
Several of the injured are believed to be seriously hurt. London Ambulance Service said a number of other people were treated at the scene for minor injuries.
Security Minister Ben Wallace said the suspect was not known to the security services, and was believed to have acted alone.
The prime minister said police declared it a terrorist incident within eight minutes and a white man in his 40s was now in custody.
Mrs May was speaking after chairing a meeting of the government's emergency Cobra committee.
"It was an attack that once again targeted the ordinary and the innocent going about their daily lives - this time British Muslims as they left a mosque having broken their fast and prayed together at this sacred time of year," she said.
She added that "there has been far too much tolerance of extremism over many years".
"It is a reminder that terrorism, extremism and hatred take many forms; and our determination to tackle them must be the same whoever is responsible."
After making her statement outside Downing Street, the prime minister visited Finsbury Park Mosque, which is also close to the scene of the incident, where she held talks with faith leaders.
Eyewitness Abdul Rahman told the BBC: "When the guy came out from his van he wanted to escape, run away, and he was saying 'I want to kill Muslims. 'I want to kill Muslims.'
"I hit him on his stomach... and then me and the other guys... we held him to the ground until he couldn't move. We stopped him until the police came."
Adil Rana, 24, said "people were punching him and beating him, which was reasonable because of what he's done".
The imam of Muslim Welfare House - which is also a community centre - said a passing police van was flagged down after the attack.
Mohammed Mahmoud told reporters: "We told them the situation - there's a man, he's restrained, he mowed down a group of people with his van and there is a mob attempting to hurt him and if you don't take him then, God forbid, he might be seriously hurt.
"We pushed people away from him until he was safely taken by police."
Toufik Kacimi, chief executive of Muslim Welfare House, said the suspect had told those holding him "you deserve it" and was also saying "I did my bit".
Another witness, who gave his name as Abdul, told the BBC the suspect was shouting "kill me, I've done my job".
Earlier, police also said the arrested man would be the "subject of a mental health assessment in due course".
Mayor of London Sadiq Khan said: "While this appears to be an attack on a particular community, like the terrible attacks in Manchester, Westminster and London Bridge it is also an assault on all our shared values of tolerance, freedom and respect."
Thee mayor has also reiterated his calls for the government to provide more funding to the Met Police.
BBC home affairs correspondent Dominic Casciani said it was not the first time that Muslims - and specifically visible Muslim targets, namely mosques - had been targeted in an act of terrorism in the UK.
The threat from extreme right-wing groups has been growing in recent years, he said, noting that 16% of all terror arrests in the year to March were classed as "domestic extremism".
At the scene
By Cherry Wilson, BBC News
Locals say this is a proudly multicultural area, where the biggest rivalry is whether you support Arsenal or their north London rivals, Tottenham.
Now the mood here is one of shock, as residents stand by the police cordon seeing the aftermath of yet another attack in London.
Mother-of-four Nicola Senior, 43, is walking back from taking her children to school when she stops to take in the scene.
She said: "I'm frightened. Is there going to be retaliation?
"I am fearful for my kids. Can we go to the park? Can we go to the church? It feels like this is happening all the time."
Forensics officers are examining a white van which has Pontyclun Van Hire on it - a firm from Rhondda Cynon Taff in south Wales.
The firm said in a statement that it was "shocked and saddened" and co-operating with the police.
A dangerous juncture in the battle against extremism
By BBC security correspondent Frank Gardner
This incident risks playing right into the hands of those planning further attacks on vulnerable citizens in the UK.
Online followers of the so-called Islamic State have been quick to seize on the Finsbury Park attack as proof of what they see as widespread hostility towards Muslims who live in the West. Inevitably, it will be used by recruiters and propagandists to incite further attacks - extremism breeds extremism.
The one thing that far right anti-Muslim extremists and violent jihadists have in common is the belief that peaceful coexistence between Muslim and non-Muslim is impossible.
The unified prayers and solidarity across communities that followed recent terror attacks are anathema to them. Extremists of both types want instead to divide society and will keep trying to bring this about by criminal acts of provocation such as this.
The Muslim Council of Britain said this was the "most violent manifestation to date" of recent Islamophobic incidents.
"We expect the authorities to increase security outside mosques as a matter of urgency."
Mohammed Kozbar, general secretary of Finsbury Park Mosque, gave a statement on behalf of a joint faiths group.
He said that "an attack on one faith is an attack on all faith and communities".
The group has appealed for calm, adding that "all of our efforts should be towards getting justice for the victims and ensuring our community stays the diverse, tolerant and welcome place we know it to be".
Home Secretary Amber Rudd described it as an appalling incident, and said new funding for security at religious sites had recently been arranged.
"We will make sure that we do all we can to reduce these sort of attacks," she added.
Labour's shadow home secretary and Hackney North and Stoke Newington MP Diane Abbott said on Twitter that police "must urgently review security for all mosques".
Labour leader and Islington North MP Jeremy Corbyn has also visited the area, telling the BBC that "an attack on a mosque, an attack on a synagogue, an attack on a church is actually an attack on all of us".
"We have to protect each other's faith, each other's way of life, and that's what makes us a strong society and community."
Mr Corbyn attended prayers at Finsbury Park Mosque with Islington Council Leader Richard Watts.
Communities Secretary Sajid Javid has also been to the area, where he met residents and community leaders.
Speaking to the BBC, he said it was a "despicable attack" which was intended to divide society, but added: "That will fail. These perpetrators will never succeed."
Mr Javid also said he wanted to reassure Muslims around the UK that the government would "always take a zero tolerance approach to hate crime".