Prime Minister Theresa May says the terror attack near a north London mosque is "every bit as sickening" as other recent ones to hit the UK.
A man drove a van into worshippers close to the Muslim Welfare House in Finsbury Park as they were gathered to help an elderly man who had collapsed.
That man later died, but it is not clear if his death was the result of the attack. Ten others were also hurt.
A 48-year-old man has been arrested on suspicion of attempted murder.
Metropolitan Police Commissioner Cressida Dick said the incident 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 were Muslim and many were believed to have just left evening prayers after breaking the Ramadan fast.
Security Minster Ben Wallace said the suspect - described by witnesses as a large, white man - was not known to the security services.
The prime minister said the driver acted alone, and police declared it a terrorist incident within eight minutes.
Mrs May was speaking after chairing a meeting of the government's emergency Cobra committee.
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.
Nine people were taken to hospital after the attack, which happened shortly after midnight, and several are seriously injured.
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".