Theresa May called the attack “every bit as sickening as those that have come before”.
She chaired a meeting of the emergency COBRA committee at Downing Street and later visited Finsbury Park Mosque in north London, near the site of the attack, meeting with community and faith leaders.
The Metropolitan Police said there will be more uniformed officers at places of worship, including mosques and Muslim community centres, as they try to reassure local people.
Speaking outside Number 10, Mrs May said the terrorist attack “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.
Mrs May 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 reopened it recently to make sure that any additional place of worship that feels the need can apply for extra security.”
The attack happened shortly after midnight, when a man drove a van into a crowd of worshippers outside the mosque, injuring nine people and leaving one dead.
A 47-year-old man has been arrested on suspicion of attempted murder and terror offences.
It is the fourth terror attack since March in the country, and the third to involve a vehicle deliberately driven at pedestrians.
It comes during the Muslim holy month of Ramadan.
For the Prime Minister, it comes at a difficult time, following her disastrous election gamble and the Grenfell Tower fire, in which dozens of people died.
Hers and the Government’s response to the blaze was widely criticised for lacking empathy. Mrs May 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 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.”