Senior German officials have called for tightened gun controls after Friday's deadly shooting in Munich that claimed the lives of nine people and the gunman, an 18-year-old reportedly obsessed with mass killings.

"We must continue to do all we can to limit and strictly control access to deadly weapons," Vice-Chancellor Sigmar Gabriel, leader of the centre-left Social Democrats, told local media on Sunday.

He said authorities were investigating how Ali Sonboly, a German-Iranian who held dual citizenship, had gained access to a weapon despite signs he had significant psychological issues.