A man detained at the scene of Friday's fatal stabbing of MP Sir David Amess is 25-year-old Ali Harbi Ali, Whitehall officials have confirmed to the BBC.
Police said the British man was being held at a London police station under the Terrorism Act 2000 and officers have until 22 October to question him.
They spent Saturday searching three addresses in the London area.
The BBC understands Mr Ali was referred to the counter-terrorist Prevent scheme a few years ago.
Prevent is the UK's terrorism-prevention programme, which aims to stop people being radicalised.
Teachers, members of the public, the NHS and others can refer individuals to a local panel of police, social workers and other experts who decide whether and how to intervene in their lives.
Engagement in the scheme is voluntary and it is not a criminal sanction.
It is thought Mr Ali, who is of Somali heritage, did not spend long in the programme - and he was never a formal "subject of interest" to the Security Service, MI5.
Officials say they do not believe any other individuals were involved in Friday's incident.
Sir David, a Conservative MP since 1983, was holding a regular Friday meeting with constituents at Belfairs Methodist Church in Leigh-on-Sea, Essex, when he was stabbed multiple times.
The 69-year-old was married with four daughters and a son. A candlelit vigil was held in Leigh-on Sea on Saturday night to mark Sir David's life.
Speaking to the gathering, Southend councillor Alan Dear said Sir David was kind, loving and gentle - "a gentleman and a gentle man".
Mr Ali was initially detained on suspicion of murder but was further detained under the Terrorism Act late on Friday.
On Saturday, detectives were granted a warrant by magistrates to allow them to keep Mr Ali in custody until Friday 22 October.
In a statement, the Met Police said a knife used in the attack was recovered at the scene. A post-mortem examination took place on Saturday, the police added.
Sir David is the second MP to be killed in recent years, following the murder of Labour MP Jo Cox in July 2016.
The latest attack has raised concerns for the safety of MPs, many of whom hold constituency surgeries which anyone can attend.
Home Secretary Priti Patel said security measures were being put in place to protect MPs - but insisted they would carry on serving the country unimpeded.
"We will carry on, we live in an open society, a democracy," she said during a visit to the scene of the attack, alongside Prime Minister Boris Johnson, Labour leader Sir Keir Starmer and Commons speaker Sir Lindsay Hoyle.
"We cannot be cowed by any individual or any motivation... to stop us from functioning, to serve our elected democracy."
Ms Patel maintained a balance could be found to allow face-to-face meetings with constituents to continue.
However, Conservative MP Tobias Elwood - who came to the aid of a stabbed police officer during the 2017 terror attack in Westminster - suggested MPs speak to constituents on the phone or over Zoom for the time being.
Labour MP Diane Abbott said she would prefer to meet constituents behind a screen to prevent possible stab attacks.
And Kim Leadbeater, the sister of Mrs Cox, said her partner had asked her to stand down as MP for Batley and Spen after Sir David's death.
Tributes to Sir David have been pouring in from politicians as well as his local constituents.
The prime minister described him as "one of the kindest, nicest, most gentle people in politics", with an "outstanding record of passing laws to help the most vulnerable".
Ms Patel called Sir David a "man of the people" who was killed doing "a job he loved".
Members of Southend-On-Sea's Muslim community said, in a joint statement, his death was an "indefensible atrocity" and that Sir David would be remembered for his warmth, selflessness and kindness.
Credit: The BBC