The attack on Amess, from Johnson's Conservative Party, comes five years after the murder of Jo Cox, a lawmaker from the opposition Labour Party, and has prompted a review of the security of elected politicians.
Amess, 69, was knifed repeatedly in the attack at about midday on Friday (October 15) in Leigh-on-Sea, east of London, during a meeting with constituents.
Police arrested a 25-year-old British man at the scene on suspicion of murder, adding it is believed he acted alone.
In a statement early on Saturday, police said the early investigation had revealed a potential motivation linked to Islamist extremism.
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.
Johnson and Starmer stood side by side in a moment of silence before leaving. On Friday, Johnson said Britain had lost a fine public servant and a much-loved friend and colleague.
As tributes poured in for Amess, politicians described the attack as an assault on democracy. Patel has said she will review the safety of elected politicians.