The attack on 69 year-old Amess, from Johnson’s Conservative Party, comes five years after the murder of Jo Cox, a lawmaker from the opposition Labour Party.
This has prompted a review of the security of elected politicians.
Amess was knifed repeatedly in the attack at about midday Friday in Leigh-on-Sea, east of London, during a meeting with constituents in a church.
Police arrested a 25-year-old British man at the scene on suspicion of murder. Police have said it is believed the man acted alone.
In a statement early on Saturday, police said the early investigation had revealed a potential motivation linked to Islamist extremism.
Later on Saturday, police said they were granted a warrant to detain the man until Friday before they have to decide whether to charge him.
Johnson, interior minister Priti Patel and Labour Party leader Keir Starmer were among those to lay flowers in tribute to Amess at the scene of the murder.
“To the memory of Sir David Amess MP, a fine parliamentarian and a much-loved colleague and friend,” Johnson said in a hand-written note placed in the flowers.
He added in a Twitter post that his thoughts were with Amess’ family and friends.
Johnson and Starmer stood side by side in a moment of silence before leaving. Other politicians, police representatives and members of the public came to lay flowers and pay respects.
As tributes poured in for Amess, politicians described the attack as an assault on democracy. Patel said security for lawmakers, known as MPs, was being reviewed and strengthened.
“All measures are being put in place for the security of MPs so that they can carry on with their duties as elected democratic members,” Patel said in a broadcast clip following the visit.
“We live in an open society, a democracy. We cannot be cowed by any individual.”
In Westminster, where lawmakers do much of their work in parliament, armed police are on patrol. But in their electoral districts, known as constituencies, more often than not there is no security.
Amess was stabbed while holding a surgery – a one-to-one meeting with voters, open to whoever turns up.
Conservative lawmaker Tobias Ellwood said that while engagement with the public was a vital part of the job, there was now huge anxiety among MPs, and he called for a pause in such meetings.
Cox, the Labour MP who was killed in November 2016, was shot and stabbed on a street in a northern England town as she arrived at an advice session with local residents.
In 2010, Labour lawmaker Stephen Timms survived a stabbing in his constituency office.
Patel said Amess was killed doing a job he loved, and lawmakers should remain accessible to the public.
“We will continue to absolutely stand by the principles that we are elected by: to serve our constituents in the open way in which we have been doing so, but also recognising that there are safety and protection measures that we have to undertake too,” Patel said.
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