The minister confirmed that Germany as well as several other Nato members had received a letter from Gates asking for troops to join the battle against Taliban fighters in southern Afghanistan but declined to comment further on its content.
Ulrich Wilhelm, a government spokesman, said Berlin found Gates's letter "surprising" and "not up for discussion".
Wilhelm said: "During all the meetings and talks we have had with the US side in recent months, the engagement of the German military in the framework of the mandate with its focus on northern Afghanistan was expressly praised.
"It was recognised that the German military is doing important, useful work there and we have always made clear that the mandate in its current form as foreseen by the parliament is the basis of our engagement in Afghanistan and that the content of this mandate is not subject to debate."
He said that Jung would raise the issue with his Nato counterparts at a meeting in Vilnius next week.
Germany currently has about 3,000 troops stationed in Afghanistan, nearly all of them deployed in the capital Kabul and the north as part of the Nato-led International Security Assistance Force (Isaf).
The parliamentary mandate rules out stationing troops in the south, where US-led troops are fighting resurgent Taliban forces.
Public support for the operation is slipping with a majority of Germans saying they oppose continued deployment in Afghanistan.
Frank-Walter Steinmeier, Germany's foreign minister, noted that Germany had stepped up its military and reconstruction efforts in the north and that its troops were making headway in stabilising the region.
|Germany has stepped up its military and reconstruction efforts in the north [EPA]|
After talks in Berlin with Carl Bildt, his Swedish counterpart, he said: "I think that is also recognised by the United States."
There are about 40,000 Nato and 20,000 US-led coalition soldiers in Afghanistan.
Nato commanders say they need about 7,500 more troops to carry out their mission.
Stephen Harper, Canada's prime minister, recently warned Gordon Brown, his British counterpart, that Ottawa would pull its 2,500 soldiers out of Afghanistan if it did not get reinforcements from other countries.