On Saturday evening police said a warrant of further detention was granted for the 25-year-old British man - who is of Somali descent. A knife used in the attack, which has been declared a terrorist incident, was recovered at the scene, the police said.
The longstanding Conservative MP was stabbed at least 17 times while he held a weekly surgery with constituents in a Methodist church in Leigh-on-Sea, Essex yesterday.
Mr Ali is not thought to have been previously known to the security services, Sky News reported.
However he was previously known to the government's Prevent scheme, which is a programme to stop radicalisation, a Whitehall source told the Guardian.
They added that his involvement with the programme was short.
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This evening police were granted permission to keep the suspect in custody until 22 October, after an extended warrant of further detention was approved by Westminster Magistrates Court.
As news of his death emerged, tributes were paid from across the political spectrum.
Home Secretary Priti Patel said Sir David was a "man of the people" who was "killed doing a job he loved".
She added: "We are all struggling to come to terms with the fact that David Amess has been so cruelly taken away from all of us.
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Prime Minister Boris Johnson and Labour leader Sir Keir Starmer both laid flowers at the scene together outside Belfairs Methodist Church this morning.
Southend borough councillor John Lamb went to the scene after hearing the MP had been stabbed shortly after midday on Friday.
He said: "The paramedics had been working on Sir David for over two and a half hours and they hadn't got him on the way to hospital.
"We knew it had to be extremely serious and that the worst scenario could occur - we were hoping it wouldn't but it did."
The 69-year-old had been an MP since 1983 and was married with four daughters and a son.
Sir David, 69, was the second serving MP to be killed in the past five years.
In 2016 Batley and Spen Labour MP Jo Cox was stabbed to death.
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