A van driven by a 48-year-old white man ploughed into a group of Muslim worshippers leaving prayers in the Finsbury Park Mosque, killing one people and injuring 10 others.
The man held by police over the attack has been identified as 47-year-old father-of-four Darren Osborne.
Khan called it "a deliberate attack on innocent Londoners, many of whom were finishing prayers during the holy month of Ramadan".
In the hours immediately following the attack, the Metropolitan Police in public statements described it as a "vehicle in collision with pedestrians".
"I would like to ... thank our Imam, Mohammed Mahmoud, whose bravery and courage helped calm the immediate situation after the incident and prevented further injuries and potential loss of life", said Toufik Kacimi, the chief executive of the Muslim Welfare House.
"As a community it is important to show that we stand together and that we will not be bowed by this attack or the others we have seen in Manchester and London in recent weeks".
"While this appears to be an attack on a particular community, like the awful attacks in Manchester, Westminster and London Bridge, it is also an assault on all our shared values of tolerance, freedom and respect", Khan said.
The incident occurred near two mosques: the Finsbury Park Mosque and the Muslim Welfare House.
Residents said they were "shocked" after seeing photographs of their neighbour being arrested in London.
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A witness, Abdiqadir Warra, told AFP that the van "drove at people" and that some of the victims were carried for several metres along the road. A vehicle struck pedestrians near a mosque in north London early Monday morni.
British Prime Minister Theresa May said the incident was "every bit as sickening" as the previous assaults that have hit Britain in recent months, including the massacre in the LondonBridge area and the May 22 suicide bombing that hit an Ariana Grande concert in Manchester.
The suspect remains in custody at a London police station. He was taken to the hospital as a precaution.
"From what we are seeing and from what witnesses have reported to us there was nobody else in the van and it appears at this time that this attacker attacked alone", Basu said. He then thanked worshippers who restrained the attacker.
British security officials, speaking on condition of anonymity in line with official policy, said hate crimes directed at Muslims have increased almost five-fold in the wake of several attacks in Britain.
He added: "I receive briefings from the counter terror team and the good news is the counter terrorism team have been recognizing for a while now there are terrorists motivated by other means other than perverse Islamist motivation". She said it was "a reminder that terrorism, extremism and hatred take many forms; and our determination to tackle them must be the same whoever is responsible".
"Diverse, welcoming, vibrant, compassionate, confident and determined never to give in to hate".
"He tried to kill a lot of people so obviously it's a terrorist attack".
It also follows a suicide bombing at a pop concert in Manchester, northern England, in May which killed 22, while in March, a man drove a rented vehicle into pedestrians on Westminster Bridge in London and stabbed a policeman to death before being shot dead.