The German ministry had also been under pressure from German commanders demanding more men after a string of attacks on soldiers and their Afghan helpers.
Jung said that extending the army's mandate to allow it to contribute up to 4,500 troops to the Nato-led International Security Assistance Force (Isaf), would give the German contingent "a little more flexibility" without necessarily
deploying the maximum number of soldiers.
Reinhold Robbe, the head of parliament's defence committee, welcomed the announcement, saying there was currently a shortfall of some 300 to 400 troops in the north.
But Jung was criticised by the Free Democrats opposition party for showing a "lack of courage" in tackling the challenges posed by the situation in Afghanistan two years into an insurgency aimed at toppling the US-backed government in Kabul.
Sending German troops into conflict zones remains a sensitive subject six decades after World War II.
Surveys have shown that ordinary Germans oppose deploying troops in southern Afghanistan and that more than half of Germans want the government to bring home its soldiers from the conflict-torn country.
Since 2002, 26 German troops have died in Afghanistan.