The 25-year-old suspect, who is believed to be a Libyan asylum seeker, was arrested at the scene of the stabbing on suspicion of murder and remains in custody.
He has been now been re-arrested under Section 41 of the Terrorism Act 2000, Counter Terrorism Policing South East (CTPSE) said on Sunday.
ITV News understands the suspect was already known to security services.
Detective Chief Superintendent Kath Barnes, head of CTPSE, said: “The investigation continues to move at a fast pace.”
She added: “Our thoughts and prayers continue to be with the families who will be mourning loved ones after this horrific act, and to all those who have been affected by it.
"We continue to work with the coroner to formally identify those who have died and to inform and support their relatives.”
The suspect was arrested within five minutes of the initial report, and a number of officers were quickly on the scene, she confirmed.
ITV News Security Editor Rohit Kachroo breaks down what else we know about the suspect, who was known to MI5
Kieran Vernon, a friend of the suspect, told ITV News he had been in his flat.
"I thought he was a decent guy, hardworking, trying to make a bit of money," he said.
"We used to meet nearly twice, three times a week, used to have a little drink as well sometimes at the park."
Counter-terrorism police took over the investigation from Thames Valley Police.
Prime Minister Boris Johnson said he is “appalled and sickened” by the terror attack and his "thoughts are very much with the family and the friends of the victims today."
Speaking in Downing Street, Mr Johnson said: "If there are lessons that we need to learn about how we handle such cases...then we learn those lessons and we will not hesitate to take action where necessary."
The head of counter terrorism policing, Metropolitan Police Assistant Commissioner Neil Basu said there is nothing to suggest anyone else was involved in the Reading attack and police are not currently seeking anyone else as part of the investigation.
Mr Basu said: "This was an atrocity."
He said police were working with the coroner to formally identify the victims and praised the actions of unarmed Thames Valley Police officers who detained the suspect, calling them "incredibly brave."
“I also want to pay tribute to the bravery of members of the public who provided emergency first aid at the scene," Mr Basu added.
Labour leader Sir Keir Starmer said this is “not a time for party politics” and that he is willing to work with the government to see if there are “lessons that can be learned” following the Reading terror attack.
He said: “It’s horrific that it happened at all wherever it happened, and across Reading, across the country there will be communities really upset and worried about this, united in their grief.
“And all of our thoughts are with those who have lost someone in this.”
The attack, which took place at 7pm on Saturday in Forbury Gardens in the town centre, also left another three people injured.
Two people have been discharged from hospital and the third remains in hospital, in a stable condition under observation.
Thames Valley Police Chief Constable John Campbell told reporters the first emergency call was made to police at 6.56pm on Saturday and that a man was arrested within five minutes.
Mr Campbell described the scene of the attack in Reading as “horrific”, which was witnessed by police officers and members of the public.
“I am sure we would all want to recognise the bravery of those police officers responding but also a number of members of the public who helped my officers and the victims at what was a very distressing scene," he added.
Mr Campbell did not identify the victims of the Reading attack and said Thames Valley Police were still in the process of contacting their next of kin.
But he said police do not believe there is a wider risk to the public and there is nothing to suggest that anyone else is involved in this incident.
Speaking to ITV News on condition of anonymity, the victim said: “I was with a group of friends - five of us just catching up, socially distanced at the park in Reading.
"Out of the blue this person suddenly showed up. He had a knife and he went forward trying to stab my face. I turned around and could see my friend had been stabbed in the back."
Deliveroo driver Amir Hadyoon, 31, said he saw the suspect arrested outside the job centre on Friar Street in Reading, a short distance from Forbury Gardens.
He said the suspect was tackled by police, telling reporters: “He wasn’t resisting or anything, even though there were like four or five police officers on top of him.
“He had a very trim beard, not much on his cheeks, he was a young guy. He had like a black T-shirt or something on, he was on the ground I couldn’t really see.
“To me it looked very weird because he didn’t say a word.”