Maas convened the government's crisis team to launch emergency measures to secure the departure of German staff and other people at risk, according to a diplomatic source.
A defence ministry spokesman did not confirm a report by tabloid Bild that two military planes were ordered to leave for Kabul later on Sunday.
Originally, several military evacuation flights were expected to depart on Monday, with the planes continuing to shuttle between Kabul and possibly the Uzbek capital Tashkent to fly out Germans and Afghans eligible for relocation to Germany.
Less than 100 Germans remain in Afghanistan beyond the government officials still working there, the foreign ministry in Berlin said on Friday.
It was still unclear on Sunday how many local helpers would be flown out.
A government source spoke of at least 1,000 former Afghan employees, including close family members, but added that this was only a rough estimate.
A support network founded by German troops put the number of those eligible for relocation under government rules at 2,000 people.
But the group, which goes by the name Patenschaftsnetzwerk Afghanische Ortskraefte (Sponsorship Network for Afghan Helpers), argues that another 4,000 Afghans should also be flown out, although they do not fulfil official requirements, as they were working as subcontractors, for example.