One of those who died has been named locally as James Furlong, a teacher at the Holt School in Wokingham.
It is understood Saadallah came to Britain several years ago as a refugee following the civil war in Libya.
Mental health is being considered a major factor in the incident, a security source said.
Armed counter terrorism police raided his flat in nearby Basingstoke Road late on Saturday night and removed a number of items including a large circular saw.
Neil Basu, the head of Counter Terror Police, said officers were not looking for anyone else in connection with the incident.
"There is no specific intelligence to suggest that anyone attending crowded places is at risk," he added.
Three people were killed and three others seriously wounded in the stabbing attack that came out of the blue Saturday in Forbury Gardens park in Reading, a town of 200,000 people 64 kilometres west of London.
Chief Constable John Campbell of Thames Valley Police said officers were called to reports of stabbings just before 7pm and arrived to find a "horrific" scene. He said a suspect was apprehended within five minutes.
Basu said "incredibly brave" unarmed officers detained a 25-year-old local man at the scene. Police said they did not believe there was any further danger to the public.
The BBC reported that Saadallah was investigated by British security services last year over concerns he planned to travel abroad to join a jihadi group, but that he was not determined to be a major threat.
Prime Minister Boris Johnson, who met security officials, police and senior ministers on Sunday for an update on the investigation, said he was "appalled and sickened" by the attack.
"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.
Police officers patrolled cordons on the roads leading to the park on Sunday, and blue-and-white tents were erected near the attack site. Overnight, heavily armed officers entered an apartment about a mile away, and a loud bang was heard.
Notes and bunches of flowers had been left Sunday by the police tape in tribute to the victims. One of the people killed was identified as James Furlong, a teacher in the nearby English town of Wokingham.
"There are no words that anyone can say to express how horrible and senseless this was," one said. ""Our prayers are with all the victims and their families and friends. #Readingstandsunited."
The attack came hours after a Black Lives Matter demonstration at Forbury Gardens, but police said there was no connection between the two events.
Personal trainer Lawrence Wort said the park was full of groups sitting on the grass Saturday evening when "one lone person walked through, suddenly shouted some unintelligible words and went around a large group of around 10, trying to stab them."
"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 running," Wort said.
Britain has been hit by several terror attacks in recent years, both by people inspired by the Islamic State group and by far-right extremists. Islamist-inspired attacks include a suicide bombing at an Ariana Grande concert in Manchester that killed 22 people in 2017 and two deadly vehicle and knife attacks in London the same year.
In several cases, attackers have been known to police. In November, a man who had been released after serving a prison sentence for a terrorism offense stabbed two people to death at a justice conference in London.
In February, a man recently released from prison after serving time for terrorism-related offenses strapped on a fake bomb and stabbed two people on a busy London street before being shot to death by police. No one else was killed.
Britain's official terrorism threat level stands at "substantial," the middle level on a five-rung scale, meaning an attack is likely.
- Daily Telegraph with AP
