The elite KSK force could see action on the ground
An opinion poll published on Wednesday found 51% in favour and 46% against Germany's involvment in the American-led military campaign.
Reservations against what would be Germany's first deployment of troops in a fighting role outside Europe since 1945 are most evident in the formerly pacifist Green Party, the junior partner in Chancellor Gerhard Schroeder's coalition.
Any deployment of German troops abroad needs Bundestag approval.
Mr Schroeder's response to a request by the United States for military support include special forces, ships, a medical evacuation unit and armoured vehicles equipped to detect nuclear, biological and chemical weapons.
Christian Stroebele, a prominet leftwinger among the Green deputies, said he could not approve such a mission: "I see no possibility at the moment of supporting participation in a war in which civilians are being killed every day."
Others within the party have expressed similar views, saying the American strategy in Afghanistan was unclear.
However, the German Foreign Minister and most prominent Green party member, Joschka Fischer, firmly supports the military mission.
Doubts have also been expressed by members of Mr Schroeder's Social Democratic Party (SPD).
One senior SPD deputy, Michael Mueller, said many within the party feared the involvement by the German armed forces was a move towards widening the conflict.
And Mr Schroeder has not given enough detail about the planned German involvement, military analysts have criticised.
One former general said the government wanted a "blank cheque", warning of the potential risks of getting drawn into a long military conflict in Afghanistan.
The government, however, is confident that the Red-Green coalition - which has a majority of 16 in parliament - will hold.
Chancellor Schroeder can also count on the support of the conservative opposition although its leaders suggested that parliament initially should limit the German deployment to six months instead of the one year Mr Schroeder wants.
Anti-war sentiments in Germany have run deep since the end of the Second World War, and for decades the country avoided any foreign military engagements.
Now several thousand German troops serve in peacekeeping missions in the former Yugoslavia.
But only last August, the governing coalition had difficulties mustering a simple majority to send 500 German soldiers to Macedonia and needed opposition votes to get the motion through.