LONDON — Declaring “enough is enough,’’ Prime Minister Theresa May vowed a sweeping review of Britain’s counterterrorism strategy Sunday, a day after the bloody rampage near London Bridge, the third major terrorist attack in the country in three months.

Although three knife-wielding men were killed during the Saturday night attack on the bridge and nearby Borough Market, investigators were racing to determine whether others assisted them.

Counterterrorism police conducted a raid at an apartment in Barking, in east London, and arrested 12 people in connection with the assault. A search continued there later Sunday.

The Islamic State’s Amaq news agency said the group’s fighters carried out the attack. ISIS, which often claims terrorism by people inspired by it, also has taken credit for last month’s Manchester Arena bombing.

At least seven people were killed and 48 more wounded in the Saturday assault, including 21 who remained in critical condition. The men sped across London Bridge in a van and rammed several pedestrians, before emerging with large hunting knives for the attack in Borough Market, a crowded nightspot.

In a matter of minutes, the three assailants were chased down by eight armed officers who fired about 50 rounds, killing the men, who wore what appeared to be suicide vests but subsequently proved to be fake. None of the assailants has been identified.

One member of the public also suffered nonfatal gunshot wounds, police said.

The assault came days before national elections this week and after the British government had downgraded the threat level to “severe’’ from “critical,’’ meaning that an attack was highly likely, but not imminent.

On Sunday morning, May’s Conservative Party and the opposition Labor Party announced they were suspending campaigning for parliamentary elections — less than a full day in the case of Labor — out of respect for the victims. The right-wing, populist, UK Independence Party said it would continue with its scheduled campaign events.

May said the election would go ahead Thursday as planned.

The prime minister led an emergency meeting of her security Cabinet on Sunday morning. In a statement afterward, she said the government would intensify its counterterrorism efforts to deal with Islamist radicalism at home and to try to restrict “the safe spaces it needs to breed,’’ both on the Internet and in British communities.

“Everybody needs to go about their lives as they normally would,’’ she said.

“Our society should continue to function in accordance with our values. But when it comes to taking on extremism and terrorism, things need to change.’’

May said the government may extend the time of custodial sentences for terrorism suspects, but more needed to be done in binding communities together to combat what she called “a perversion of Islam,’’ adding, “There is, to be frank, far too much tolerance of extremism in our country.’’

May, who was home secretary for six years before becoming prime minister, has been pressing for a tougher line against Islamist extremism for some time.

By stating that police and security measures were insufficient, she was announcing a new effort, if reelected, to break down what she considers to be essentially self-segregated communities and to be less delicate of their sensitivities.

Legally, she has been stymied by the difficulty of finding a definition of “extremism’’ that would hold up in court when challenged on the grounds of free speech.

May also called for a global effort to “regulate cyberspace,’’ something that is likely to prove difficult, and said that the London attack was not connected to a suicide bombing at the pop concert in Manchester last month that killed 22 people.

Britain’s home secretary, Amber Rudd, said Sunday that the government was confident the London attackers were “radical Islamist terrorists’’ but was still trying to determine their affiliations.

“As the prime minister said, we are confident about the fact that they were radical Islamist terrorists, the way they were inspired, and we need to find out more about where this radicalization came from,’’ Rudd said on ITV television.

She refused to say whether the attackers had been known to authorities before Saturday.

A resident of the neighborhood on King’s Road in Barking, where the apartment was raided Sunday, said that he knew the man who lived in the apartment with his wife and two young children, and said his neighbor looked to be in his mid-20s and was known in the community by his nickname, “Abs.’’

“He would always be in a religious gown to his shins, with tracksuit bottoms and trainers underneath,’’ the resident, Ken Chigbo, 26, said about his neighbor, with whom he played table tennis. “I trusted him. We got on.’’

Chigbo added that a group of three to four men would visit his neighbor’s apartment every week or so. “I found them quite intimidating, actually,’’ he said. “They were always in religious robes and wearing red-and-white checkered scarves wrapped around their heads.’’

London Mayor Sadiq Khan said police had been dispersed across the city, as security would remain heightened throughout the week.

Khan, who described the assault as a “deliberate and cowardly attack on innocent Londoners,’’ said some of the injured were in critical condition, raising the possibility that the death toll could rise. “We will never let these cowards win and we will never be cowed by terrorism,’’ he said.

The Muslim Council of Britain also condemned the attack and praised the emergency services.

“Muslims everywhere are outraged and disgusted at these cowards who once again have destroyed the lives of our fellow Britons,’’ said the council’s secretary general, Harun Khan.

The city of London will hold a public vigil Monday evening for the seven people killed in the attack. It will be at Potters Fields Park, which surrounds City Hall on the River Thames.

The attack hit a nation still recovering from the shock of the bombing in Manchester almost two weeks ago, when a suicide bomber blew himself up outside the doors of an Ariana Grande concert. Many of those killed were children, and 116 people were injured.

Grande returned to Manchester with a star-powered lineup Sunday night to perform in a charity concert and pay tribute to the victims.

Saturday’s attack was reminiscent of another on Westminster Bridge on March 22, when Khalid Masood, 52, drove a car into pedestrians, killing four people. He then stabbed a police officer to death before being shot and killed near Parliament. Police treated that attack, in which 50 were injured, as “Islamist-related terrorism.’’

Prime Minister Justin Trudeau of Canada said a Canadian citizen was among those killed in Saturday’s attack. Among the wounded were citizens of Australia, France, Germany, and Spain.

President Trump said on Twitter, “Whatever the United States can do to help out in London and the UK, we will be there — We are with you. God bless!’’

But then the president took aim at political correctness and Khan.

“We must stop being politically correct and get down to the business of security for our people,’’ he posted. “If we don’t get smart it will only get worse.’’

Chancellor Angela Merkel of Germany said, “We are united beyond all borders in horror and sorrow, but also in determination.’’