The man arrested for the murder of MP Sir David Amess has been named as Ali Harbi Ali.
The 25-year-old is not believed to have been previously known to security services.
The British national with Somali heritage was arrested after Conservative MP for Southend West Sir David Amess was stabbed at a constituency surgery on Friday.
Detectives have been granted a warrant of further detention at Westminster Magistrates' Court which allows them to hold a man on suspicion of the murder of until October 22.
In a statement, Scotland Yard said: "Late on Friday, whilst in police custody, the man was subsequently further detained under section 41 of the Terrorism Act 2000 and he is now being held at a London police station.
"On Saturday, detectives were granted a warrant of further detention at Westminster Magistrates' Court, allowing them to keep the man in custody until October 22, when the warrant expires.
"As part of the fast-paced investigation, officers have attended three addresses in the London area and conducted searches. One of these searches has concluded and the others are ongoing. A post-mortem examination has taken place today."
Labour and the Liberal Democrats will not stand candidates in the by-election contest to find a successor to David Amess.
It comes after a Labour peer and former minister urged major opposition parties to honour past precedent by refusing to battle for the Southend West seat following the fatal stabbing of the Tory incumbent.
Meanwhile, The Home Secretary has said politicians will not be "cowed" following the fatal stabbing of MP Sir David Amess, which police believe may be linked to Islamist extremism.
Priti Patel visited the scene at Belfairs Methodist Church in Leigh-on-Sea on Saturday morning alongside Prime Minister Boris Johnson, Labour leader Sir Keir Starmer and Commons Speaker Sir Lindsay Hoyle to pay their respects to Sir David, less than 24 hours after he was killed at a constituency surgery.
Ms Patel said security measures were being put in place to protect MPs but vowed they will carry on serving the country unimpeded in the face of the attack, which the Metropolitan Police have declared was a terrorist incident.
Speaking at Southend Police Station, the Home Secretary said: "We will carry on, we live in an open society, a democracy. We cannot be cowed by any individual or any motivation... to stop us from functioning, to serve our elected democracy."
Asked whether there could be a balance between the safety of MPs and the democratic process, she said: "It can be balanced, it can absolutely be balanced."
Ms Patel said Sir David was "was killed doing a job that he loves, serving his own constituents as an elected democratic member and, of course, acts of this... are absolutely wrong, and we cannot let that get in the way of our functioning democracy."
"So that is why there are measures under way right now - I convened meetings yesterday, I've been with the Speaker of the House, and with the police and our security services to make sure that 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," she added.
