Theresa May, who didn't disclose the man's name, said that he was once investigated for extremism links, but was considered a peripheral figure.
The revelation came moments after Parliament held a minute of silence and reconvened less than 24 hours after Wednesday's brutal attack, which killed three victims and forced a lockdown of the British government's seat of power.
May delivered a defiant message to the House of Commons, declaring simply: "We are not afraid."
In a sweeping statement, she set an unyielding tone, promising answers as to why a British-born national drove an SUV into innocent pedestrians along Westminster Bridge before charging into a parliamentary courtyard and stabbing a police officer. Police shot and killed the attacker.
While she honored the police, she also saluted the everyday actions of millions who went about their lives in London as normal and describing it as proof that the attack failed to break the determination of Londoners and Britons.
"As I speak millions will be boarding trains and airplanes to travel to London, and to see for themselves the greatest city on Earth," she told the House. "It is in these actions - millions of acts of normality - that we find the best response to terrorism —a response that denies our enemies their victory, that refuses to let them win, that shows we will never give in."
Parliament began its moment of silence at 9:33 a.m. (5:33 a.m. EDT), honoring the slain police officer, 48-year-old Keith Palmer, a 15-year veteran of the Metropolitan Police and a former soldier. Parliament then returned to business, an act of defiance to those who had attacked British democracy.
"Those who carry out such wicked and depraved acts as we saw yesterday can never triumph in our country and we must ensure it is not violence, hatred or division but decency and tolerance that prevails in our country," Trade Secretary Liam Fox said.
"Hear, hear!" lawmakers from all parties responded in unison.
Authorities know the identity of the man who went on the car and gun rampage at Parliament on Thursday, but police and the prime minister didn't disclose his name.
Police believe that the man acted alone and there is no reason to believe "imminent further attacks" are planned, she said.
Mayor Sadiq Khan called for Londoners to attend a candlelit vigil at Trafalgar Square on Thursday evening in solidarity with the victims and their families and to show that the city remains united.
Parliament Square, Westminster Bridge and several surrounding streets remain cordoned off by police. Scores of unarmed officers in bright yellow jackets were staffing the perimeter tape, guiding confused civil servants trying to get to work. In Parliament's New Palace Yard, a blue police tent was erected over the spot where the stabbing and shooting occurred, and two forensic officers worked at a trestle table nearby.
Metropolitan Police counterterrorism chief Mark Rowley revised the death toll from five to four, including the attacker, the police officer and two civilians. He said that 29 people required hospitalization and seven of them were in critical condition. He also said that authorities were still working out the number of "walking wounded." Police had previously given the total number of injured as around 40.
One of those killed was Aysha Frade, a British national whose mother is Spanish, the Spanish Foreign Ministry said.
A doctor who treated the wounded from the bridge said some had "catastrophic" injuries. Three police officers returning from a ceremony to honor their bravery were among the injured.
May said people from 11 countries were among the victims. They included: 12 Britons, 3 French, 2 Romanians, 4 South Koreans, 1 German, 1 Pole, 1 Irish, 1 Chinese, 1 Italian, 1 American and two Greeks required hospital treatment. Police earlier said that seven of the 29 who are hospitalized are in critical condition.
The threat level for international terrorism in the U.K. was already listed at severe, meaning an attack was "highly likely."
President Donald Trump was among world leaders offering condolences.
London has been a target for terrorism many times over past decades. Just this weekend, hundreds of armed police took part in an exercise simulating a "marauding" terrorist attack on the River Thames.
May said underscored that the attack targeted "free people everywhere," and she said she had a response: "You will not defeat us."
"Let this be the message from this House and this nation today: our values will prevail," she said.