A terror suspect held over the knife attack in a Reading park that killed three people came to the attention of MI5 last year, security sources have said.
The 25-year-old man, understood to be named Khairi Saadallah, was detained a short distance from the scene at Forbury Gardens and arrested on suspicion of murder.
He was later re-arrested under Section 41 of the Terrorism Act, which gives police the power to detain him without charge for up to 14 days.
School teacher James Furlong, 36, is the only victim to be named so far.
Two other people injured in the attack remain in hospital, while one has now been discharged.
It emerged on Sunday the suspect, a refugee of the civil war in Libya, briefly came to the attention of MI5 last year, but the information provided did not meet the threshold of investigation.
PA understands from security sources that M15 had received intelligence he planned to travel abroad, possibly for terrorism purposes, but the threat was found to be insubstantial.
As counter-terror officers investigate, mental health is understood to be considered a major factor in the latest incident.
Police have said they are not looking for anyone else in connection with the attack.
Prime Minister Boris Johnson said he was "appalled and sickened" by the incident and said "we will not hesitate to take action" if there are lessons to be learned from the circumstances.
The suspect was jailed in October for a complex series of non-terror offences before his sentence was reduced to one of 17 months and 20 days' imprisonment in the Court of Appeal.
One of the appeal judges who gave the judgment in March, Mr Justice Goss, noted Saadallah's various mental health issues in reducing the sentence.
Saadallah was released from prison earlier this month, it is understood, and the Covid-19 pandemic played no part in the decision to free him.
The Sun reported that he left HMP Bullingdon, Oxfordshire, 17 days ago after less than half of his sentence.
Tributes from former students of Mr Furlong poured in after a letter from the two co-head teachers at his school – the Holt School in Wokingham – announcing his death was circulated online.
His parents, Gary and Janet, said in a statement: "He was the best son, brother, uncle and partner you could wish for.
"We are thankful for the memories he gave us all. We will never forget him and he will live in our hearts forever."
Security guard Sydney McDonald, 65, who saw suspect being rugby-tackled to the ground by police described how it looked as if he had put his hands "in a big bucket of red paint".
He told the PA news agency: "I had just finished work at about 7.10pm and as soon as I came out of the shop, there were about four police cars, they turned around in the middle of the road, they were driving pretty fast.
"There was a guy and I saw him pointing to a man and saying 'There he is, there he is'. If he hadn't, they would have missed him. He was running really fast, properly fast.
"They put the emergency brakes on, jumped out of the car and rugby-tackled him to the floor. He was on his stomach and the blood on his hands looked like he had put his hand in a big bucket of red paint.
"They put the handcuffs on, he wasn't putting up a fight or anything like that, they picked him up and put him in the van, he just sat there all quiet, he wasn't saying nothing."
Personal trainer Lawrence Wort, 20, who said he was around 10 metres from the incident, told PA on Saturday night the suspect was alone and "shouted some unintelligible words" before launching the attack.
"He went around a large group of around 10, trying to stab them," he said.
"He stabbed three of them, severely in the neck, and under the arms, and then turned and started running towards me, and we turned and started running."
Thames Valley Police have pleaded with the public not to share any pictures or images of the killings on social media, and instead contact them on 101, or upload the footage to UKPoliceImageAppeal.co.uk.
Despite treating the incident as a terror attack, Metropolitan Police Assistant Commissioner Neil Basu said on Sunday the motive is still "far from certain".
Mr Basu said there was no evidence to suggest anyone attending crowded places is at risk, but asked people to "be alert, not alarmed, when you are in public".