Essex police said officers had responded “within minutes” to reports of the stabbing shortly after 12:05pm (1105 GMT) and arrived to find Amess had “suffered multiple injuries”.
“This was a difficult incident, but our officers and paramedics from the East of England Ambulance Service worked extremely hard to save Sir David,” Harrington said.
“Tragically he died at the scene.”
A father-of-five who was first elected to parliament in 1983, Amess was memorialised with an impromptu evening mass while tributes poured in from across the political spectrum and around the world.
Multiple UK media outlets, citing sources, reported that the suspect was believed to be a British national with Somali heritage.
“The investigation is in its very early stages and is being led by officers from the specialist counter-terrorism command,” Ben-Julian Harrington, Essex police’s chief constable, told reporters.
“We made it clear at the time of the incident that we did not believe there was any immediate further threat to anyone else in the area,” Harrington said.
The killing has sent shockwaves around Britain.
Flags were lowered to half-mast in Westminster as tributes were paid to Amess, whose death came five years after the murder of Labour party MP Jo Cox by a far-right extremist.
In a book last year called “Ayes & Ears: A Survivor’s Guide to Westminster”, Amess noted that Cox’s death had prompted new security guidance to lawmakers that threatened to limit their access to constituents.
“This sort of thing just was not supposed to happen in the UK,” he wrote about Cox’s killing.
“These increasing attacks have rather spoilt the great British tradition of the people openly meeting their elected politicians.”
Prime minister Boris Johnson said Amess was “a much-loved friend and colleague” and “a fine public servant”.
“The reason I think people are so shocked and saddened is above all he was one of the kindest, nicest, most gentle people in politics.”
Dozens of local community members honoured their elected representative in a mass held at another Leigh-on-Sea church near the crime scene on Friday evening.
“He died doing the thing he loved -- meeting his constituents,” said Jeff Woolnough, a priest who led the liturgy.
‘Attack on democracy’
All Britain’s living former prime ministers also paid tribute to Amess, including Theresa May, who called it “a tragic day for our democracy”.
Prince William and his wife Kate said the couple were “shocked and saddened” and noted Amess had “dedicated 40 years of his life to serving his community”.
Condolences also came from the United States, Canada and Spain.
“An attack on elected officials is an attack on democracy,” US Secretary of State Antony Blinken tweeted.
Britain’s House of Commons speaker Lindsay Hoyle said Amess had “built a reputation for kindness and generosity” during his long parliamentary career.
“In the coming days, we will need to discuss and examine MPs’ security and any measures to be taken, but for now, our thoughts and prayers are with David’s family, friends and colleagues,” Hoyle added.
Interior minister Priti Patel’s spokesman said she had chaired a meeting of police, security and intelligence agencies and “asked all police forces to review security arrangements for MPs with immediate effect”.
‘Cowardly as it gets’
Amess was first elected during Margaret Thatcher’s tenure and was known for his advocacy of animal welfare and pro-life issues.
He had advertised Friday’s “surgery” -- an open meeting for constituents -- at the Belfairs Methodist Church in Leigh-on-Sea.
While public attacks on British MPs are not common, lawmakers have been the victims of stabbings in the past.
In January 2000, Liberal Democrat MP Nigel Jones was wounded and his assistant killed by a man wielding a ceremonial sword at a surgery.
Pro-EU MP Cox was killed in the run-up to the Brexit referendum, while another Labour MP, Stephen Timms, was stabbed multiple times during an event in 2010 but recovered and is still a lawmaker.
Timms said he was “appalled” at this latest attack.
Cox’s widower Brendan said it was “as cowardly as it gets”.