Thomas de Maiziere, who is to visit Morocco, Algeria and Tunisia, said many applicants lacked travel documents or gave false names and other personal details, making it more difficult to send them back to their countries of origin.
Modern technology such as biometric identity papers could help, he told AFP, adding that "we could imagine offering our support" in the area.
"Our goal is to make the procedures more efficient and faster," he said in written responses to AFP questions ahead of his departure for Morocco later Sunday.
After taking in more than one million asylum seekers last year, Germany is trying to reduce arrivals, including with a law to declare Morocco, Algeria and Tunisia safe countries of origin.
A similar designation adopted for several Balkans countries raised the bar for asylum applications and sharply reduced the influx from the region of what Germany considers "economic refugees".
Arrivals from North Africa jumped in late 2015 but in January dropped off to 1,600 each from Morocco and Algeria and 170 Tunisians, according to government data.
Human rights groups have opposed a "safe" designation for the three Maghreb countries under a law awaiting upper house approval, pointing to discrimination against homosexuals and curbs on free speech and assembly.
De Maiziere rejected the criticism, saying that although designated safe countries are assumed to not systematically persecute their citizens, individual requests for protection would still be considered.
Chancellor Angela Merkel has come under intense pressure to limit the influx, mainly from war-torn Syria, Iraq and Afghanistan, with the southern state of Bavaria demanding permanent controls on its border with Austria.
State premier Horst Seehofer has repeatedly called for a cap on arrivals and charged in comments to news weekly Der Spiegel that "the country is divided. The people are unsettled, polarisation is on the rise."
Bavaria's interior ministry has instructed police to work out a scenario for quickly deploying thousands of officers to shut the border, public broadcaster Bayerischer Rundfunk reported.
Merkel received high praise, however, for her liberal migrant policy from World Bank chief Jim Yong Kim
Kim called her welcome to people fleeing war and desperation "very inspiring", according to Welt am Sonntag newspaper, and described her as one of the "most extraordinary" world leaders.