Armed police at railway stations in London are now a familiar sight but they are being joined today by 1,000 troops.
Premier League champion Chelsea has called off its victory parade because of the concert attack in Manchester.
The bomb used in the attack appeared to contain carefully packed shrapnel and have a powerful, high-velocity charge, according to leaked photographs from the investigation.
Manchester-born Abedi went to school locally and then studied business management at Salford University, before dropping out from the course.
He said police want the approach to be "unpredictable" and to make London "as hostile an environment as possible to terrorists". Neighbors recalled him as a tall, thin young man who often wore traditional Islamic dress and did not talk much.
They were arrested "after police executed warrants in South Manchester", the Greater Manchester Police department says.
Grande did not give a specific date in her post for her return to Manchester, but promised to share details as soon as everything is confirmed.
Some bands - including Blondie and Take That - canceled shows after the blast but representatives for several music acts - including Celine Dion, Shawn Mendes, Guns N' Roses and Phil Collins - said they will honor their European dates this summer. "I was really shocked when I saw the news, I still don't believe it", he said in Libya's capital.
The police and security services will be given time and all the resources they need to establish these facts.More news: More than 100 civilians killed in Iraq bombing in March
British Prime Minister Theresa May said earlier she would tell Trump that intelligence shared between their two countries had to remain secure, in a rare public show of dissatisfaction with Britain's closest security ally.
She also complained about US officials leaking sensitive information about Abedi to the press. Rudd said Britain's operational security could be harmed by the leaks, taking "the element of surprise" away from security services and police.
TRT World's Jon Brain reports on the latest from Manchester.
Labour leader Jeremy Corbyn plans to use a speech Friday to link Britain's actions overseas to the increased extremist threat at home.
Officials said all those hospitalized had been identified.
Rudd said up to 3,800 soldiers could be deployed on Britain's streets, taking on guard duties at places like Buckingham Palace and Downing Street to free up police to focus on patrols and investigation.
Greg Katz in London and Angela Charlton in Paris contributed.