Merkel's conservative Christian Democrats and sister Bavarian-only Christian Social Union parties met throughout the day with the pro-business Free Democrats and the traditionally left-leaning Greens. The four parties are trying to establish the framework for a coalition never before tried at the national level.
They had hoped to agree Thursday whether to start formal coalition negotiations, but said they now are aiming for a resolution before Monday.
The Greens have faced opposition to a demand for Germany to end its use of coal and combustion engines by 2030, although party leaders have signaled they would be open to a compromise.
The other parties are committed to reducing carbon emissions, but Merkel's bloc hasn't put a date on when to phase out coal. The Free Democratic Party has expressed concern about what the moves would mean for jobs and Germany's economic competitiveness.
A dispute over whether immigrants who have received protection but not full asylum in Germany should be allowed to bring close relatives to the country has been a bigger sticking point.
The Greens argue that extending family sponsorship rights would not result in many more immigrants and would help those already in Germany better integrate. The Christian Social Union, in particular, is against any loosening of the family reunification policy.
A decision to open coalition negotiations would require approval from Greens members at a party congress later this month, so any compromise would have to be something party leaders could sell to their membership.
Failure to reach a coalition agreement could result in a new election. The center-left Social Democrats, Merkel's partners in the outgoing government, have been adamant about going into opposition after a disastrous result in the Sept. 24 election.
Polls so far suggest that a new vote would produce a very similar parliament to the current one, making efforts to form a new government similarly difficult.
German President Frank-Walter Steinmeier urged all sides to avoid pushing the country back to the polls. He told the Welt am Sonntag newspaper he does not think any political parties are eager for another election.
Steinmeier, a former Social Democrat who is now unaffiliated with a political party according to the tradition for German presidents, said it was also good that the sides were tackling issues important to the public.
"If the ... negotiators are battling hard now over questions like migration and climate protection, that isn't necessarily bad for democracy," he said.
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