Suspected Copenhagen gunman was known to be 'at risk of radicalisation'
The Prison and Probation Service reported in September that the 22-year-old was at "risk of radicalisation", while he was serving time for a stabbing, the Security and Intelligence Service (PET) said in a statement.
However, it added: "PET had, against the background of the alert from the Prison and Probation Service no reason to believe that the now deceased 22-year-old offender was planning attacks."
The suspected gunman, identified by the media as Omar El-Hussein, a Danish-born man of Palestinian origin, was killed in a shootout with police on Sunday.
Danish politicians have called for an investigation into whether police and the intelligence services could have done more to head off the weekend attacks that left two people dead.
"I assume the government will review this information. Have mistakes been made on the part of the police or PET? That has to be made clear," the main opposition party Venstre's spokesman on justice issues, Karsten Lauritzen, told the Berlingske newspaper.
Police are on high alert after the shootings at a cultural centre and a synagogue in Copenhagen that have stoked fears in Europe about increasing anti-Semitic attacks.
An area around the site of the first attack was cordoned off on Tuesday after the discovery of a "suspicious" letter but the cordon was subsequently lifted after no explosives were found.