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.