His run-ins with the law regarded threats, property damage, fraud and a hit-and-run, but Adomeit said that all charges were dismissed.
"The assailant has tried before to commit suicide", according to ZDF TV channel while Süddeutsche Zeitung, a German daily newspaper said that the authorities have not found elements proving that it was a terror attack, reports Midi Libre.
Reul said two people were killed in the crash and the driver killed himself lower than the earlier police toll of three dead plus the driver.
At least 20 people were injured, and some of them were airlifted to nearby hospitals for treatment.
Germany has been on especially high alert for jihadist attacks after several claimed by the Islamic State group.
And in Spain, the jihadists also claimed a rampage along Barcelona's Las Ramblas boulevard in August 2017 that killed 14 and left more than 100 injured.
As per witnesses, the people were seen running all over moments after the attack. He said the suspect was a German citizen and that investigators are still working to establish a motive. It showed pictures of where police had cordoned off an area of the city.
Police have appealed to the public for information about the attack, setting up a website where people can upload photos or videos. "The investigations are being conducted at full speed and on all fronts", he added.
"This was a frightful and sad day for the people of Muenster, all of Germany ... and also the people of The Netherlands, who were sitting here and became victims", he said.
They are investigating "all possible avenues", said the north-western city's senior prosecutor, Martin Botzenhardt. The Interior Ministry in North Rhine-Westphalia, where Muenster is located, would neither confirm nor deny the Sueddeutsche report. "Everything possible is being done to investigate the act and support the victims and their families".
The motivation of the attack remained unclear so far, while some German media reported that the perpetrator could be psychologically disordered.
Inside the man's apartment, which was near the crash scene and raided late on Saturday, police found more firecrackers and a "no longer usable AK-47 machine gun".
Munster is a popular tourist destination with 300,000 inhabitants, known for its medieval old town, which was rebuilt after massive destruction during the Second World War.
It happened as people were eating outside a restaurant in the city's historic centre just before 3.30pm on Saturday afternoon.