He told the crowd "an attack on one faith is an attack on us all".
They had been helping a man who had collapsed.
"Extra police resources have already been deployed to reassure communities, and police will continue to assess the security needs of mosques and provide any additional resources needed", she said.
France's antiterrorism prosecutor is investigating.
According to a tweet from Transport for London, Seven Sisters Road has been closed northbound at Hornsey Road and southbound at Rock Street. After the Westminster attack in March it took police just over two hours to do so.
They were visibly shocked when informed. Jo Stevens, the member of Parliament for the Cardiff Central constituency, issued an appeal to the public for any information about him, but also urged people to refrain from online speculation.
Rabbi Herschel Gluck said the incident was an attack on "every single Muslim in the United Kingdom and beyond". "No one place is safe in the world". "It was my birthday last night", she said.
Victoria Boucher and daughter Chrystel said they're hoping the Champs-Elysees reopens soon. Muslim leaders called for calm. "We will stay a strong city", the mayor said.
"The show must go on", the daughter said in English.
After the London Bridge attack, the mayor's office reported a 40-percent increase in racist incidents in the capital and a five-fold increase in anti-Muslim incidents.
Gerard Collomb says he will present a bill Wednesday at a Cabinet meeting to extend the state of emergency from July 15, its current expiration date, until November 1.
Mrs May said security was being stepped up. The previous attacks had been blamed on Islamist extremists. The three Islamic extremists who carried out the attack were killed by police.
The interior minister said the man was killed in the incident.
Police said the attacker who drove the van has been arrested on suspicion of the commission, preparation or instigation of terrorism, including murder and attempted murder. "It was just a normal voice, he just said it", Nadeem told the Guardian.
Bomb squad officers are at the scene on the city's most famous avenue, which is popular with tourists.
No police officers or passers-by were hurt in the afternoon assault.
He was pronounced dead at the scene at 1:04am. He was heard to yell that he wanted to "kill all Muslims" or "kill more Muslims" or possibly both.
Brandet said bomb squads were still securing the scene.
France's anti-terrorism prosecutor has opened an investigation into the ramming of a police vehicle on Paris' Champs-Elysees avenue.
Ms Sharazi said she believed the comment was not meant with ill intent and was the first conflict they had encountered with their neighbour. Early police caution about declaring the incident to be terrorist-related was interpreted by the community as discriminatory.
The driver of the van jumped out of the vehicle and tried to run, Aidroos said.
"This was an attack on Muslims near their place of worship", May said in a televised address.
Neighbors and people in the area have had similar reactions. Paris police said neither gendarmes nor passers-by were injured.
'He is bleeding out of his ear, but in general his health was stable, ' he told the Press Association after visiting his uncle in hospital. That man later died but it is not yet clear if that was due to the terror attack. The officials weren't authorized to be publicly named.
A man could be seen lying on his stomach on the ground immediately after the incident, wearing a white shirt and dark shorts.