Three other people were injured during the attack at 7pm on Saturday in Forbury Gardens in Reading town centre.
A man who went on a stabbing rampage in Reading, England, killed three people and injured three more.
Police said they arrested a man at the scene.
Police officers were standing guard on Sunday outside the corridor of a top-floor flat in Basingstoke Road, Reading, where the suspect in the Forbury Gardens stabbings was detained.
The National Police Chiefs' Council has called against "speculation or sharing of video or images of the serious incident in Reading", advising that the curious follow Thames Valley Police updates on the situation.
Prime Minister Boris Johnson has already held a meeting about the incident with security officials, police and senior ministers, Downing Street said.
This is a developing story. About a dozen armed police officers with shields were seen entering the block and families living in the building were moved out. The same man reportedly also was charged previous year with assaulting a judge who had sentenced him.
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However, a Reading man of the same reported name and age as the suspect was sentenced to two months in prison a year ago for assaulting an emergency worker, The Associated Press reported.
In a statement released Sunday, Head of Counter Terrorism Policing Neil Basu said the individual remains in custody and is thought to have acted alone.
"Officers from Counter Terrorism Policing South East have been working closely with Thames Valley Police's Major Crime Department throughout the night", the counter-terrorism police said in a statement.
"There is no intelligence to suggest that there is any further danger to the public, however we urge people to remain vigilant and report anything suspicious by calling police", he added.
Nieema Hassan, an organiser of the Reading BLM protest, said that demonstrators had already dispersed by the time the attack occurred.
As the attacker headed for another group, the witness and his friends ran from the park.
"If there are lessons that we need to learn" or legal changes needed to prevent such attacks, "then we will learn those lessons and we will not hesitate to take action where necessary", Johnson said. "I would just really ask that people stay alert as they were before".
Past year the government downgraded the national terrorism threat level to "substantial", meaning an attack is likely, from "severe".
Airline worker Carlos Garcia Pascual was walking to his home near Forbury Gardens when emergency vehicles and police officers descended.