A man held on suspicion of stabbing three people to death in a British park at the weekend was known to the security services, media reported on Monday.

The 25-year-old, widely identified as Khairi Saadallah, a Libyan refugee, was held on suspicion of murder on Saturday night, soon after the rampage in Reading, west of London.

Thames Valley Police then re-arrested him under the Terrorism Act 2000, which allows for detention without charge for up to 14 days.

Witnesses to the attack in Forbury Gardens described seeing a lone assailant walking through a park filled with people and stabbing them at random.

British media said Saadallah fled the civil war in Libya and had been released from prison earlier this month, after serving time for a series of non-terror offences.

He briefly came to the attention of the domestic intelligence agency MI5 last year and was said to have planned to travel abroad, reportedly to Syria.

But he was not deemed to be a substantial risk. His mental health is understood to be a factor for investigating officers.

Mark Rowley, a former assistant commissioner for specialist operations in the Metropolitan Police, said Saadallah would have been one of thousands of people on MI5's watch list.

Some 3,000 people are under investigation at any one time but there are up to 40,000 people who have come up on the radar in relation to extremist ideology, he told BBC radio.

"To spot one of those who is going to go from a casual interest into a determined attacker... is the most wicked problem that the services face," he added.

The reports about the suspect's time in prison will again raise questions about the early release of offenders after two previous terror attacks in the past year.

In November, a convicted jihadist on parole was shot dead by police after stabbing five people -- two fatally -- near London Bridge in the heart of the British capital.

Armed officers also shot dead another assailant who injured three people in a London stabbing attack in February. He had also been released early from a terrorism conviction.

Those attacks prompted Prime Minister Boris Johnson's government to tighten the law on early prison releases.

A second, named as Joe Ritchie-Bennett, was said to have moved to Britain from Philadelphia in the United States some 15 years ago.

US Ambassador to Britain Woody Johnson offered condolences to everyone affected. "To our great sorrow, this includes an American citizen," he wrote on Twitter.

Security Minister James Brokenshire said that despite the attack, Britain's terrorist threat level remains unchanged at "substantial", which means an attack is deemed "likely".

"People must remain vigilant," he told the BBC.

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