Discord broke out in German Chancellor Angela Merkel's ruling coalition Sunday, after the United States urged the country to send ground troops to Syria as Washington looks to withdraw from the region.
"We want ground troops from Germany to partly replace our soldiers" in the area as part of the anti-Islamic State coalition, US special representative on Syria James Jeffrey had told German media including Die Welt newspaper.
Jeffrey, who was visiting Berlin for Syria talks, added that he expects an answer this month.
Last year US President Donald Trump declared victory against IS and ordered the withdrawal of all 2,000 American troops from Syria.
A small number have remained in northeastern Syria, an area not controlled by the regime of President Bashar al-Assad, and Washington is pushing for increased military support from other members of the international coalition against IS.
"We are looking for volunteers who want to take part here and among other coalition partners," Jeffrey said.
A clear rejection of the American request came from Merkel's junior coalition partners, the Social Democrats (SPD).
"There will be no German ground troops in Syria with us," tweeted a member of the interim SPD leadership, Thorsten Schaefer-Guembel.
"I don't see people wanting that among our coalition partners" in Merkel's centre-right CDU, he added.
But deputy conservative parliamentary leader Johann Wadephul told news agency DPA that Germany should "not reflexively reject" the US call for troops.
"Our security, not the Americans', is being decided in this region," added Wadephul, seen as a candidate to succeed Ursula von der Leyen as defence minister if she is confirmed as European Commission chief.
Syria's war has killed more than 370,000 people and displaced millions since it started in 2011 with a brutal crackdown on anti-government protests.
This isn't a banana republic
Washington has two goals in northeastern Syria: to support the US-backed Kurdish forces that expelled IS from northern Syria as they are increasingly threatened by Turkey, and to prevent a potential IS resurgence in the war-torn country.
The US is hoping Europe will help, pressuring Britain, France and now Germany, which has so far deployed surveillance aircraft and other non-combat military support in Syria.
However Germany's history makes military spending and foreign adventures controversial.
Berlin sent soldiers to fight abroad for the first time since World War II in 1994, and much of the political spectrum and the public remains suspicious of such deployments.
As well as the SPD, the ecologist Greens, liberal Free Democrats and Left party all urged Merkel to reject the US request for troops.
The US appeal comes after Trump has repeatedly urged Berlin to increase its defence spending, last month calling Germany "delinquent" over its contributions to NATO's budget.
But such criticisms have more often hardened resistance to forking out more on the military rather than loosening the country's purse strings.
Former Chancellor Gerhard Schroeder told business newspaper Handelsblatt on Saturday that Trump wanted "vassals" rather than allies.
"I'd have liked the federal government to tell him once or twice that it's none of his business" how much Germany spends on defence, Schroeder said.
"This isn't a banana republic here!"