Assistant deputy Commissioner Dean Haydon, the senior national coordinator for the fight Against the Terrorism of the Police network, said the attack a terrorist incident, and Counter-Terrorism Police South-East will be taking over the investigation, Thames Valley police said.
A security source told the Guardian that the suspect had been granted asylum.
Boris Johnson, the prime minister, chaired a meeting at 9am on the Sunday morning, 10 to be updated on the latest developments, Downing Street said.
“The PM has been updated on the ongoing investigation into the fatal stabbing in Reading yesterday,” a spokesman said.
The interior minister, Priti Patel was present, as well as the police and security officials.
Home office sources said that the suspect is a Libyan national.
Johnson, Patel, and the labour leader, Keir Starmer, were among the senior leaders have expressed their condolences to the family and friends of the victims.
DCI Ian Hunter said: “We made a stop, and at this stage we are not seeking any other persons in connection with this incident.
“There is no intelligence that there was no more danger to the public. However, we urge people to remain vigilant and report anything suspicious by calling the police.”
TB officers were seen in a group of officers entering a block of flats in the Reading understood to have been the suspect at his home.
More than a dozen armed police officers carrying shields were seen entering the block at about 11 o’clock in the evening.
There were several witnesses to the attack, which took place at 7pm in the popular Forbury Gardens, home to the Maiwand Lion statue, the image of which has been adopted by the Reading football club and Reading the Post newspaper.
Disturbing videos on social media showed scenes of victims receiving resuscitation treatment.
Lawrence Wort, 20, a personal trainer, said he was about 10 meters of the attack.
“The park was pretty full, lots of people sitting around drinking with friends, when only one person to cross suddenly cried out a few unintelligible words, and went around a large group of around 10, trying to stab them,” he told reporters.
“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 to run.
“When he realized that he could not catch us, he tried to stab another group sat down. He had a person in the back, the neck, and then, when he realized, everyone began to run, to run out of the park”.
Claire Gould, a freelance journalist who lives near the scene, said PA Media, she has seen air ambulance, emergency ground vehicles on the nearby Kings Prairie, a police helicopter circled overhead.
She described hearing sirens and said surrounding roads and a retail park had been cordoned off by officers.
At least two of the wounded were treated in the emergency department of the Royal Berkshire Hospital.
The prime minister earlier tweeted: “My thoughts are with all those affected by the terrible incident in the Reading and my thanks to the emergency services on the scene.”
The minister of the interior said in a statement: “This evening we have seen a senseless attack on the people simply enjoy a Saturday evening with family and friends. My heart, prayers and thoughts are with all those affected and to the people of Reading who will be deeply shocked and concerned by this terrible incident.
“I am in contact with the police and ensure that they have the support they need. I would like to thank Thames Valley police and the emergency services for their response.”
Thames Valley police said the incident was not linked to a Black Lives Matter protest that took place in the Reading, earlier in the day.