A senior member of the Muslim community in Manchester and a law enforcement official who requested anonymity said Mr. Abedi had been barred from the mosque in 2015 for expressing his support for the Islamic State, and he came to the attention of intelligence agencies at the time as “a person of interest.”

In raising the threat level, Mrs. May cited information gathered Tuesday in the investigation into the Manchester bombing and said the Joint Terrorism Analysis Center, the body responsible for setting the level, would continue to review the situation.

“The change in the threat level means that there will be additional resources and support made available to the police as they work to keep us all safe,” Mrs. May said.

“I do not want the public to feel unduly alarmed,” she said. “We have faced a serious terrorist threat in our country for many years, and the operational response I have just outlined is a proportionate and sensible response to the threat that our security experts judge we face.”

It was only the third time that Britain had raised the threat level to critical.

The first was on Aug. 10, 2006, after the government foiled a plot to blow up trans-Atlantic airliners with liquid bombs. The second was on June 30, 2007, after two men slammed an S.U.V. into entrance doors at Glasgow Airport and turned the vehicle into a potentially lethal fireball.

After the prime minister’s announcement, Assistant Commissioner Mark Rowley, the head of National Counter Terrorism Policing, said in a statement that “we are flexing our resources to increase police presence at key sites, such as transport and other crowded places, and we are reviewing key events over the coming weeks.”