Armed police have arrested eight people in raids linked to the rampage that left three people dead.
"An act of terrorism tried to silence our democracy," May told a packed House of Commons, which stood for a minute's silence in remembrance of the victims of Wednesday's strike on the symbol of Britain's democracy.
"We are not afraid and our resolve will never waver in the face of terrorism," May said.
Armed police have arrested eight people in raids linked to the rampage that left three people dead and sowed panic in the heart of London.
The IS group said it was responsible, according to the Amaq propaganda agency linked to the jihadist organisation.
"The perpetrator of yesterday's attack in front of the British parliament was a soldier of the Islamic State and the operation was carried out in response to calls to target coalition countries," Amaq said citing a "security source."
Defiant British lawmakers returned to "business as usual" in the surreal silence of an area of central London normally thronged with tourists.
Twenty-nine people were treated in hospital, including seven in critical condition, some with "catastrophic" injuries. Among them were French school children and foreign tourists.
The attacker mowed down pedestrians with a car on Westminster bridge, killing two, and then jumped out and stabbed to death a police officer guarding parliament before being shot dead.
The carnage was unleashed on the same day Brussels was marking the anniversary of Islamic State group bombings that killed 32 people.
Hundreds of extra police were on patrol in London as officers worked around the clock to piece together what happened in the deadliest attack in Britain since four suicide bombers killed 52 people on the capital's transport system in July 2005.
Europe has been on high alert after a wave of deadly jihadist assaults over the past two years.
May said the attacker's identity was known to the police and the MI5 domestic intelligence service.
He was British-born and some years ago had been a "peripheral figure" investigated over concerns about violent extremism.
"There was no prior intelligence of his intent -- or of the plot," May said.
Britain's top anti-terror officer Mark Rowley said that police had arrested eight people in raids on six houses in London, the central city of Birmingham and elsewhere.
"It is still our belief... that this attacker acted alone yesterday and was inspired by international terrorism," he said.
Defence Secretary Michael Fallon told BBC radio the working assumption was that the attack was linked to "Islamic terrorism in some form".
The British flag over parliament flew at half-mast in a sign of mourning while forensic officers in white suits carried out a fingertip search of the courtyard outside where 48-year-old policeman Keith Palmer was stabbed to death.
Police officers lined up outside their new headquarters nearby for a minute's silence in front of the eternal flame to officers who have given their lives in service.
Queen Elizabeth II was due to open the building formally on Thursday but postponed the visit.
"My thoughts, prayers, and deepest sympathy are with all those who have been affected by yesterday's awful violence," she said, in a statement expressing her "enduring admiration" for the police.
London Mayor Sadiq Khan called a candlelit vigil on Trafalgar Square later Thursday.
Among those in parliament was Foreign Office minister Tobias Ellwood, whose face was left smeared with blood after giving first aid to the fatally wounded police officer.
US President Donald Trump and French President Francois Hollande both spoke to May and Chancellor Angela Merkel said Germany stood with Britons "against all forms of terrorism".
Britain's last terror attack was the 2016 assassination of MP Jo Cox by a pro-Nazi sympathiser in her constituency in northern England shortly before the vote to leave the European Union.
That vote triggered a push in Scotland for a second referendum on seceding from the United Kingdom.
The Scottish Parliament has postponed a debate and vote on the referendum following the London attack.
The debate is now due to resume on Tuesday, the day before Britain is set to trigger the Article 50 two-year departure process for leaving the EU.
May's spokesman said there was no intention to delay Article 50 because of Wednesday's attack.
A Spanish diplomatic source confirmed that one of the dead was 43-year-old British citizen Aysha Frade, whose mother was Spanish.
Media reports said she was on her way to pick up her two daughters, aged seven and nine, from school.
A man in his 50s was also killed.
Several international tourists visiting one of London's most iconic sights were also caught up in the violence.
Those wounded included 12 Britons, four South Koreans, three French children, two Romanians, two Greeks and one each from China, Germany, Ireland, Italy, Poland and the United States, May said.
Three police officers were among those hurt, two of them seriously, and a seriously injured woman was rescued from the River Thames after coming off the bridge.
French Foreign Minister Jean-Marc Ayrault travelled to London to visit three French pupils on a school trip who were among those hurt.