The Prime Minister met with communty leaders at Finsbury Park mosque after she chaired a meeting of the emergency COBRA committee at Downing Street.
Speaking outside Number 10, she said the Finsbury Park attack was "every bit as sickening as those that have come before" and "targeted the ordinary and the innocent going about their daily lives".
"Today we come together as we have done before to condemn this act and to state once again that hatred and evil of this kind will never succeed," she added.
She said security was being stepped up.
"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.
The Government last summer announced a fund devoted to the security of places of worship, Home Secretary Amber Rudd said.
"We have made available £2.5m," she told Sky News.
"I recently announced who would be getting those additional funds, which included 12 mosques, and actually I have repoened it recently to make sure that any additional place of worship that feels the need can apply for extra security."
In the latest attack to hit Britain, a man drove a van into a crowd of worshippers outside the mosque, injuring 10 people and leaving one dead.
A 48-year-old man who had been held by members of the public was arrested on suspicion of attempted murder.
It is the fourth attack since March in the country, and the third to involve a vehicle deliberately driven at pedestrians.
The attack comes during the Muslim holy month of Ramadan.
For the PM, it comes at a difficult time, following her disastrous election gamble and the Grenfell Tower fire, in which dozens of people were killed.
Her and the Government's response to the blaze was widely criticised for lacking empathy. The PM did not meet any survivors when she first visited the scene of the fire, and was heckled when she returned a day later.
Mrs May is fighting for her survival amid rumours a leadership challenge might be imminent.
Communities Secretary Sajid Javid also visited the scene, and, outside the police cordon, comforted a woman who was visibly shaking.
Mr Javid said: "I want to reassure both the local Muslim community, but also Muslims across the United Kingdom, that they will always have the full support of this government in fighting anti-Muslim hate crime."
Jeremy Corbyn, who lives near the site of the attack, expressed "absolute shock".
After meeting with faith leaders at the Finsbury Park mosque, the Labour leader called the attack "an act of terror against a wholly innocent community who were coming out of prayers and walking home on the street next to where I live".
"I am of course critical of cuts made to the police service, I make no criticism of the police behaviour or reaction last night."
More follows...(c) Sky News 2017: May visits Finsbury Park Mosque near scene of terror attack