The Bilateral Security Agreement (BSA) which would allow some US troops to stay in Afghanistan after 2014 was approved by a loya jirga, or tribal assembly, last November.
But it hit the buffers when President Hamid Karzai made a surprise decision not to sign it.
More than 50,000 combat troops from the US-led NATO force are due to pull out by the end of this year.
But Washington is proposing that around 10,000 US soldiers are deployed from 2015 to train and assist Afghan security forces in their battle against Taliban militants.
NATO members and allies considering deploying troops after 2014 have been waiting on the US-Afghan pact to negotiate their own legal arrangements with Kabul for their forces.
"It is important that [the BSA] be signed immediately" for the maintenance of German troops in Afghanistan after 2014, Foreign Minister Frank-Walter Steinmeier told reporters.
He was speaking at a joint news conference with his Afghan counterpart Zarar Ahmad Usmani after meeting Karzai in Kabul.
The German government decided on Wednesday to extend by ten months its military presence in the country until the end of 2014. The lower house of parliament, the Bundestag, must still give its approval.
It is the first visit to Afghanistan by the Social Democrat minister since he entered the coalition government of Chancellor Angela Merkel that emerged from September's elections.
It comes as the United Nations said the number of civilians killed and wounded in Afghanistan rose by 14 percent last year.
A total of 8,615 civilian casualties were recorded in 2013, with 2,959 killed and 5,656 wounded, according to the United Nations Assistance Mission in Afghanistan's annual report.
More than 50,000 NATO-led combat troops who are still in Afghanistan are due to leave by the year-end.