Steinmeier, who arrived in the Afghan capital on Saturday, held talks with both presidential candidates Abdullah Abdullah and Ashraf Ghani.
"He invited the two (candidates) to work towards a solution rapidly as there is not much time," a source within the German delegation accompanying Steinmeier said.
The minister called for a "government that capable of acting" and "rapid decisions".
Both presidential candidates claim to have won the June 14 election, triggering a political stalemate and rising ethnic tension as US-led NATO combat troops withdraw after 13 years of fighting the Taliban.
The United Nations has said results of an audit into the polls should be finalised by September 10, with the delayed inauguration of President Hamid Karzai's successor scheduled to be held soon after.
Ghani and Abdullah reportedly told Steinmeier that "negotiations between the two parties on the possible formation of a national unity government made some progress but there remains many difficult political questions that have not been answered"