BERLIN (Reuters) - If Angela Merkel becomes German chancellor again, nearly half of voters would want her to quit her term early, according to a poll offering a rare sign that domestic support for Europe’s most influential leader may be waning.

German Chancellor Angela Merkel holds a candle as she attends the inauguration of memorial at the site of last year's truck attack in a Christmas market, which killed 12 people and injured many others, at Breitscheidplatz square in Berlin. REUTERS/Fabrizio Bensch

Merkel’s conservatives won a national election in September, setting her up for a fourth stint in office.

But they bled support to the far right, and talks on a three-way coalition with the Greens and the pro-business Free Democrats collapsed in November.

Merkel is now pinning her hopes on cutting a deal with the center-left Social Democrats (SPD), who finished second in the election but have so far given a lukewarm response to the idea of renewing the ‘grand coalition’ that governed Germany between 2013 and 2017.

The YouGov survey, commissioned by Germany’s DPA agency and published in Wednesday’s Die Welt newspaper, showed 47 percent of respondents wanted Merkel to step aside before 2021, when her fourth term would end - up from 36 percent in a poll taken at the beginning of October.

By contrast, 36 percent want her to serve a full four years, compared to 44 percent three months ago.

The SPD, which lost ground among voters after the coalition with Merkel, has been reluctant to commit to a re-run as it looks to keep a skeptical rank and file on board.

SPD Foreign Minister Sigmar Gabriel, a former leader of the party, adopted a tough tone on Wednesday in top-selling daily Bild.

“If the chancellery continues to reject all the proposals for EU reform, there will be no coalition with the SPD,” he told the paper.

The SPD’s current leader, Martin Schulz, has championed deeper euro zone reform, calling for a United States of Europe by 2025.

Gabriel also said the conservatives needed to reform the health system to close the gap between private and state care.

An INSA poll in Bild put Merkel’s conservatives up 2 points at 33 percent and the SPD down 0.5 percent at 20.5 percent.

The far-right Alternative for Germany (AfD) which, capitalizing on voters’ fears about growing inequality and the impact on Germany of Europe’s migrant crisis, entered parliament for the first time in September, was down 1 point at 13 percent.

Many commentators have suggested the AfD would make gains if new elections were held due to a failure on Merkel’s part to form a government.

Merkel’s conservatives and the SPD have said they will start exploratory coalition talks on Jan. 7.