Three people were killed and three others were seriously injured in the stabbings which took place at 7pm on Saturday in Forbury Gardens. A 25-year-old man from Reading was arrested at the scene on suspicion of murder and is currently in custody.
In a statement, Mr Basu said: “Let me be clear that there is no specific intelligence to suggest anyone else attending crowded places is at risk.
“So I would ask the public to continue in your daily lives but to be alert, not alarmed, when you are in public places.”
Mr Basu added that there is nothing to suggest anyone else was involved in the attack.
He said: “From our inquiries undertaken so far, officers have found nothing to suggest that there was anyone else involved in this attack and presently we’re not looking for anyone else in relation to the incident.
“However, counter-terrorism detectives work closely with the security services and will work closely with Thames Valley major crime colleagues and we continue to make inquiries to ensure that is the case.
“Although the motivation for this horrific act is far from certain, counter-terrorism policing have taken responsibility for leading the investigation.
“However we’re clear that it was not associated in any way with the Black Lives Matter protest which took place peacefully earlier on in the day.”
Mr Basu also praised the “bravery” of police officers and members of the public at the scene.
“I also want to pay tribute to the bravery of members of the public who provided emergency first aid at the scene.”
Thames Valley Police said on Sunday morning the attack is being treated as terrorism and that counter-terrorism police would now be taking over the investigation.
Chief Constable John Campbell of Thames Valley Police said: “Incidents of this nature are very rare, though I know that will be of little comfort to those involved and understand the concern that this incident will have caused amongst our local community.
“We will be working closely with our partners over the coming days and weeks to support the Reading community during this time, as well as with Counter-Terror Police South East (CTPSE) as they progress their investigation.”
Prime Minister Boris Johnson said he is “appalled and sickened that people should lose their lives in this way and our thoughts are very much with the family and the friends of the victims today”.
Mr Johnson added: “I’ve obviously talked to the chief constable at Thames Valley Police, thanked him and his officers for their bravery in tackling the suspect.
“We now have someone in custody. The police must get on with their job, get to the bottom of exactly what happened, and so it would be difficult really to comment in detail.
“Except to say this, if there are lessons we need to learn about how we handle such cases, how we handle the events leading up to such cases, then we will learn those lessons and we will not hesitate to take action where necessary.”