However, Security Minister Ben Wallace said there was no evidence of a specific threat over Britain's holiday weekend, when major events will take place including Saturday's soccer FA Cup final in London, where extra armed officers will be on duty.
As U.K. election campaigning resumed following Monday's deadly bombing in Manchester, Labour Party leader Jeremy Corbyn used a high-profile policy speech to also draw a link between British foreign policy and terror attacks.
"We must be fearless enough to admit the "war on terror" is not working".
At the launch of the UK Independence Party's manifesto on Thursday, deputy leader Suzanne Evans said May, a former interior minister, "must bear some responsibility" for the terror attack in Manchester this week due to policing budget cuts.
May was speaking to reporters at a summit of Group of Seven leaders in Sicily where she won support for action to prevent militants from using the internet to spread propaganda.
Police said a man was arrested in the Moss Side area of Manchester in the early hours of Friday and another man held earlier was released without charge. A New York Times spokeswoman said in a statement that its coverage of the bombing was "both comprehensive and responsible" and that the paper had strict guidelines on how to cover sensitive stories.
Libya said it was working closely with Britain to identify possible "terrorist networks" involved, while a British official said that Abedi had been on the intelligence radar before the massacre.
British police arrested two more people and searched a new site in Manchester suspected of links to the concert bombing that left 22 people dead, as British authorities complained bitterly Thursday about investigation leaks blamed on U.S. officials.More news: Palestinians, Israel police clash at Jerusalem Old City gate
So far 10 people have been arrested at addresses in Manchester, Wigan and Nuneaton, all in England.
British officials say that have receive assurances from US authorities that confidential material will be protected. Tillerson said the allies' close security relationship would survive. "There is no way of guessing what will happen in the two weeks to polling day, but we will be able to be more confident about how voting intention settles down over the next few days".
Corbyn, a veteran peace campaigner, also linked British foreign policy to domestic terrorism, saying that Labour would "change the way we do things abroad" if it wins power.
Many experts, including professionals in our intelligence and security services, have pointed to the connections between wars our government has supported or fought in other countries and terrorism here at home.
Opponents accused Corbyn of politicizing the Manchester attack. "To suggest that there is any link, that there is any justification, for the events that took place on Monday night in Manchester with United Kingdom foreign policy is outrageous", Rudd said.
But then she said: "If there is a need for troops to supplement armed officers then of course we accept that". However, with nearly 20,000 fewer police than when the Conservatives came to power in 2010, concern about police cuts is now likely to become a major issue in the election campaign. "We think in the end as well as global intervention, you've got to have negotiation", Abbott said. "Does the government not expect this?" one voter, who was not named, asked Rudd on the BBC's Question Time program on Thursday night.
May called the snap election to strengthen her hand in negotiations on Britain's exit from the European Union.