Federal prosecutors who deal with terrorist cases said they planned to take over the investigation against the 55-year-old man, who remained in a coma after emergency surgery for multiple bullet wounds.
The man had sparked major panic around noon on Monday when he stormed a McDonald's restaurant inside Cologne's central railway station armed with a petrol container, a replica pistol and gas canisters with metal balls taped to them, police said.
The dishevelled-looking man with long grey hair poured the petrol onto the floor and set it alight, injuring a 14-year-old girl with burn wounds and sparking the alarm that led authorities to quickly evacuate the busy station and stop all trains.
As smoke and screams filled the room and the sprinkler system activated, he ran into a nearby pharmacy and took a female employee hostage, sparking an hours-long drama and tense negotiations with police.
Witnesses reported that the man had claimed to be a member of the Islamic State jihadist group, and police said they were investigating whether his motive was “terrorism” and whether he acted alone or with others.
When the suspect threatened to set fire to his terrified hostage, heavily armed police commandos hurled two stun grenades into the shop and opened fire, hitting the Syrian man with multiple bullets.
When police later searched his room in a refugee shelter, they found more petrol containers and the Arabic message “God is greatest” written on the wall, but no references to the IS or other militant groups.
Investigators confirmed that the man was indeed the holder of a Syrian passport found at the scene, and said he had drawn police attention 13 times since he arrived from the war-torn country in March 2015.
His offences included marijuana possession, theft, threatening behaviour, fraud and disturbing the peace, said Klaus-Stephan Becker, head of Cologne criminal police.
Becker confirmed that “there is evidence” the man had psychological problems and was unable to work.
The man's wife had remained in Syria, from where she had unsuccessfully launched two asylum requests to Germany.
Germany remains on high alert over the risk of a jihadist attack, having suffered several in recent years.
The bloodiest, claimed by IS, was a truck rampage through a Berlin Christmas market in December 2016 that left 12 people dead.