"The investigation has revealed a possible motive linked to Islamist extremism," the police wrote in a statement on their website.
According to the police, the country's national coordinator for counter-terrorism, Dean Haydon, has decided that the case should be considered a terrorist act.
A 25-year-old man was arrested shortly after the act near the church where Amess was stabbed yesterday at lunchtime.
He is being held by police in Essex County, east of London.
Addresses in London are being investigated
Police believe the 25-year-old acted alone.
Two addresses in the London area have been investigated by the police during the night.
David Amess was at Belfair's Methodist Church in Leigh-on-Sea to meet voters when he was stabbed.
He later died of his injuries.
Member of Parliament for 38 years
Amess was elected to parliament in 1983 and belonged to the Conservative Party.
He was a devout Catholic and a staunch opponent of abortion, but also strongly committed to animal welfare issues and an opponent of fox hunting.
He belonged to the party's Brexit phalanx.
The Prime Minister of the United Kingdom Boris Johnson commented on the act on Friday night.
"David was a man who believed in his country and its future, we have lost an honorable person in the public service, a much-loved friend and colleague," Johnson said.
David Amess has been a member of the British House of Commons since 1983. Photo: Richard Townshend