The gruesome van-and-knife rampage in London spurred calls Sunday on both sides of the Atlantic for further homefront offensives in the war on terrorism, with Prime Minister Theresa May endorsing a crackdown on pockets of Islamic extremism in the United Kingdom and President Trump renewing his push for a temporary travel ban in the U.S.
British police arrested a dozen people in the wake of the attack, in which three men in a van mowed down pedestrians late Saturday on London Bridge and then went on a stabbing rampage in a nearby market neighborhood.
The three terrorists — one of whom was reported to have screamed, “This is for Allah” — were gunned down by police.
In eight horrific minutes, seven people were killed and 48 others wounded. British police said 21 remained in critical condition Sunday night.
The Islamic State claimed responsibility in a statement distributed through its Amaq News Agency, saying the attack was carried out by “a detachment of Islamic State fighters.”
Mrs. May, who faces an election Thursday, said the third major attack in two months demanded tougher counterterrorism measures, including closing down terrorist websites and ending Britain’s longtime tolerance of extremism in Muslim communities.
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“It is time to say, ‘Enough is enough,’” Ms. May said outside No. 10 Downing St. “When it comes to taking on extremism and terrorism, things need to change.”
While authorities do not believe the three recent attacks were coordinated, the prime minster said, “They are bound together by the single, evil ideology of Islamist extremism that preaches hatred, sows division and promotes sectarianism.”
Mrs. May said the elections would proceed as planned.
Her call for a crackdown on radical Islamic recruiters on the internet was echoed in the U.S. by Sen. Lindsey Graham, South Carolina Republican and a leading defense hawk.
“There’s a gap in our laws,” Mr. Graham said. “We’re going to have to take down their recruiting networks. We have to look at the fact that we are at war and part of the battlefield is in cyberspace.”
The bloodshed in London was the third terrorist attack in the U.K. in two months, including a suicide bombing less than two weeks ago at an Ariana Grande concert in Manchester that killed 22 people, many of them girls and young women.
The attacks, taking place during the Islamic holy month of Ramadan, also occurred just over two months after a deadly car-and-knife attack outside the British Parliament.
In defiance of the London Bridge attack, Miss Grande went ahead with a planned benefit concert Sunday night in Manchester.
The “One Love Manchester” concert featured a galaxy of pop stars including Justin Bieber, Katy Perry, Coldplay, Miley Cyrus, Take That, Pharrell Williams, Black Eyed Peas, Niall Horan and Robbie Williams. The event raised money for victims of the bomb attack at Miss Grande’s earlier concert.
“We’re stronger than we’ve been before,” Miss Grande belted out from the stage.
After the Manchester attack, Britain raised its threat level to “critical” — meaning an attack was expected imminently — but downgraded it back to “severe,” which means an attack was highly likely, eight days before the London Bridge attack.
In London, the investigation continued and a large police cordon remained in place on the bridge and on the south of the Thames River in the Borough Market neighborhood.
Police determined that one of the attackers had rented the large white van. The three terrorists, who wore fake explosive vests, were not identified.
“We have already made significant progress, but of course, there remains much more to do,” said Metropolitan Police Assistant Commissioner Mark Rowley.
He said all of the attackers were killed at the scene, but investigators continued to search for accomplices and others involved prior to the attack.
Among the injured were a British Transport Police officer and an off-duty officer, he confirmed.
The eight police officers who encountered the knife-wielding terrorists shot about 50 rounds of ammunition that killed the three men. A bystander also was hit by the gunfire and was being treated at a hospital for what were believed to be minor gunshot wounds, said Mr. Rowley.
“The situation these officers were confronted with was critical — a matter of life and death: Three armed men, wearing what appeared to be suicide belts, had already attacked and killed members of the public and had to be stopped immediately,” he said. “I am humbled by the bravery of an officer who will rush toward a potential suicide bomber thinking only of protecting others.”
Mr. Trump, who spoke Saturday night with Mrs. May to offer condolences and U.S. assistance, said on Twitter that the violence underscored the need for the U.S. Supreme Court to uphold his travel ban, which lower courts have blocked.
“We need to be smart, vigilant and tough. We need the courts to give us back our rights. We need the Travel Ban as an extra level of safety!” he said.
Mr. Trump warned that political correctness was standing in the way of improved security.
“We must stop being politically correct and get down to the business of security for our people. If we don’t get smart it will only get worse,” he tweeted.
The travel ban and the attack on political correctness were prominent elements of his campaign last year, thrilling supporters who ultimately put him in the White House but outraging political opponents on the left.
Mr. Trump, in comments at a fundraising gala Sunday night at Ford’s Theatre in Washington, said he would do whatever it takes to prevent such carnage in the U.S.
“This bloodshed must end,” he said.
“We renew our resolve, stronger than ever before, to protect the United States and its allies from a vile enemy that has waged war on innocent life,” Mr. Trump said.
Sen. Mark R. Warner, Virginia Democrat and vice chairman of the Senate Select Committee on Intelligence, admonished the president for the tweet. He said America’s tradition of tolerance and integrating newcomers was the “secret sauce” that prevented more London-style attacks from happening in the U.S.
“I think we are seeing, again, the benefits of that,” Mr. Warner said on CNN’s “State of the Union” program. “That’s why it troubled me so much to see the type of tweets the president has put out in the last 12 hours.”
Mr. Trump also caused a flap by blasting London Mayor Sadiq Khan, who is a Muslim, on Twitter for his measured response to the deadly attack.
“At least 7 dead and 48 wounded in terror attack and Mayor of London says there is ‘no reason to be alarmed!’” he tweeted.
The president appeared to take out of context Mr. Khan’s quote about increased police presence in London.
“Londoners will see an increased police presence today and over the course of the next few days. There’s no reason to be alarmed,” the mayor said in a BBC interview.
Mr. Khan’s spokesman dismissed Mr. Trump’s tweet as “ill-informed,” BuzzFeed reported.
“The mayor is busy working with the police, emergency services and the government to coordinate the response to this horrific and cowardly terrorist attack and provide leadership and reassurance to Londoners and visitors to our city. He has more important things to do than respond to Donald Trump’s ill-informed tweet that deliberately takes out of context his remarks urging Londoners not to be alarmed when they saw more police — including armed officers — on the streets,” said the spokesman.
• Ken Shepherd contributed to this article, which is based in part on wire service reports.