"You will understand that with four apartments - two in eastern Germany, two in Muenster - we can't now say conclusively that we won't find anything", he said.
The statement spoke only of "several" arrests but a tweet by the police mentioned six arrests carried out by special forces.
Bode said six of the 20 injured were in severe condition.
Prosecutors said he had expressed suicidal plans by email to a neighbor.
Elke Adomeit told reporters the Muenster authorities had three criminal proceedings against him while there was a further charge against him with the Ansbach prosecutor.
They also requested the public via Twitter to avoid speculating on the cause of the incident.
Police searched four properties that were linked to the suspect and said that they found "no clues" that suggested a political motive.
German Chancellor Angela Merkel says she is "deeply shocked by the awful events in Muenster".
Armin Laschet, the governor of North Rhine-Westphalia state where Muenster is located, toured the city Sunday.
"This was a disgusting and sad day for the people of Munster, all of Germany. and also the people of the Netherlands, who were sitting here and became victims", he said. Twelve people, including the man driving the truck when it was hijacked, were killed. The German news agency dpa reported that witnesses spoke of two others in the van besides the driver.
So far the 48-year-old German who killed two and injured 20 - some seriously - with a van before shooting himself has been identified only as Jens R.
In a joint statement with police, prosecutor Martin Botzenhardt wrote Sunday that, "as of now, we don't have any leads regarding a possible background for the deed". "The investigations are being led under high pressure in all possible directions".
Investigators named the victims as a 51-year-old woman from the Lueneburg area in northern Germany and a 65-year-old man from the Borken area near Muenster. Their names were not released, as is customary in Germany.
The driver of the vehicle, who has not yet been officially identified, but is believed to be a German citizen, shot and killed himself at the scene, according to authorities.
Armed Police officers are seen at the scene when several people were killed and injured when a auto ploughed into pedestrians in Muenster, western Germany on April 7, 2018.
Police in the university city of 300,000 did not immediately confirm the reports. NPR's Esme Nicholson says the incident was in the city's historic center.
The vehicle ploughed into people seated at tables in the old city centre of Muenster, a popular tourist destination.