"There is a new suspect we are searching for — he is a suspect but not necessarily the assailant," the minister told reporters.
He declined to immediately confirm numerous media reports that the suspect was a Tunisian asylum seeker with links to the Islamic extremist scene.
However, a conservative lawmaker at the same news conference, Stephan Meyer, said the suspect was in fact from Tunisia and being watched by police.
"We are apparently talking about a potentially dangerous suspect who was known to authorities and belonged to the Salafist-Islamist scene," he told reporters after a meeting of parliament's interior affairs committee.
Meyer, of Chancellor Angela Merkel's Christian Democrats, said the case underlined his party's drive to see Tunisia, Morocco and Algeria as "safe countries of origin" whose citizens would not normally be granted asylum.
Media reports said asylum office papers believed to belong to the Tunisian man were found in the cab of the 40-tonne lorry used in the attack that killed 12 people.
Germany this year moved to declare Algeria, Morocco and Tunisia as safe countries of origin, to raise the bar for asylum requests after last year's record influx of around 890,000 people.
But the bill has been stuck in the Upper House for months over human rights concerns in those countries.
Germany this year moved to declare Algeria, Morocco and Tunisia as safe countries of origin, to raise the bar for asylum requests after last year's record influx of around 890,000 people.
But the bill has been stuck in the Upper House for months over human rights concerns in those countries.