LONDON— Authorities said 21 people remained in critical condition Sunday after a rampage at the iconic London Bridge and a nearby market that left seven dead and dozens more injured.

Three suspected terrorists also were killed in Saturday night's attack, the third in Britain in less than three months. Police said 12 people were arrested Sunday, although their alleged connection to the attack was not revealed.

"It is time to say enough is enough," Prime Minister Theresa May said Sunday. She called for tougher measures to contain Islamic extremism, saying the recent attacks are not directly linked, but “terrorism breeds terrorism.”

“They are bound together by the single evil ideology of Islamist extremism that preaches hatred, sows division and promotes sectarianism,” she said. “It is an ideology that claims our Western values and freedom, democracy and human rights are incompatible with the religion of Islam."

The SITE Intelligence Group says Islamic State's news agency is claiming fighters for the extremist group carried out the van and knife attack in London that left seven people dead.

SITE said in a statement Sunday that the Islamic State's Aamaq news service cited "a security source" in the Arabic-language posting claiming the attack.

Islamic State has often made such claims not just when it has sent attackers, but when extremists carrying out deadly plots were inspired by the group's ideology.

Police said a van plowed into pedestrians on London Bridge, then drove to the nearby Borough Market where the assailants went on a stabbing rampage. Armed officers confronted three suspects, who police said were wearing "hoax" suicide vests, at the market. All three were shot dead.

Counterterrorism police units made the arrests during a sweep in the East London community of Barking, and more homes in the area were being searched, police said.

READ: Social media reacts to terror attacks

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Mark Rowley, head of counterterrorism for Metropolitan Police, said all the attackers are thought to be dead. He said eight officers fired about 50 shots, and that one member of the public suffered a gunshot wound. That person's injuries were not believed to be critical, he said.

Rowley lauded the courage of officers who ran toward the attack as it unfolded.

"I am humbled by the bravery of an officer who will rush toward a potential suicide bomber thinking only of protecting others," he said.

Some of the 48 wounded and taken to local hospitals had life-threatening injuries, and 36 remained hospitalized late Sunday, police said. Among them was a British Transport Police officer in stable condition after showing "enormous courage in the face of danger, as did many others who were at the scene and rushed to help," Chief Constable Paul Crowther said. An off-duty London police officer also was injured.

London Mayor Sadiq Khan said he was "appalled and furious that these twisted and cowardly terrorists deliberately targeted innocent Londoners" and tourists. He urged all Londoners to "remain calm and vigilant today and over the days ahead."

President Trump tweeted solidarity with Britain, saying: "WE ARE WITH YOU. GOD BLESS!" But Trump also took shots at political correctness and gun control.

“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,” Trump tweeted.

The secretary general of the Muslim Council of Britain, Harun Khan, also condemned the attack.

“Muslims everywhere are outraged and disgusted at these cowards who once again have destroyed the lives of our fellow Britons," he said "That this should happen in this month of Ramadan, when many Muslims were praying and fasting, only goes to show that these people respect neither life nor faith."

Photos: Police at London Bridge after car reportedly plows into people

Daniel Ansah, 50, a security guard at Tito's restaurant near London Bridge, was present when the attack unfolded. He and others at the restaurant helped some of the wounded.

"It was horrific," he said. "I saw about three people running to the market and there were about five people on the floor."

He said he believed there were more than three attackers. Some of the wounded pleaded for help, Ansah said.

"Two men said, 'Help me.' They had gunshot or stab wounds on their backs and the blood was flowing," Ansah said. "It could have happened to me, too. I'm traumatized."

Four French citizens were among the wounded. French President Emmanuel Macron denounced the “abominable and cowardly” attack and said France will continue fighting “terrorism with all our strength alongside Britain and all other countries concerned.”

Britain has weathered two other terrorist attacks in recent months. On March 22, five people were killed in London after Khalid Masood rammed his car into pedestrians on Westminster Bridge before fatally stabbing a policeman outside Parliament. Masood was shot dead by police. The Islamic State said a "soldier" from the group carried out the attack. Police later said Masood had no links to extremist groups such as al-Qaeda or the Islamic State, also known as ISIS.

On May 22, Salman Abedi, a British-born suicide bomber, killed 22 people and injured 59 others at an Ariana Grande concert in Manchester in northwestern England. Abedi died at the scene. ISIS claimed responsibility but that claim cannot be verified.

Saturday's attack came on the eve of a benefit concert that Grande will hold in Manchester for victims of last month's bombing to aid the victims and their families. Police said Sunday's concert will still take place, with additional security.

"We're deeply saddened to hear about last night's horrific attacks in London and our thoughts are with everyone affected," said Greater Manchester Police's Assistant Chief Constable Garry Shewan.

Candidates in Thursday's parliamentary elections suspended campaigning on Sunday but will resume on Monday.