BERLIN — The impasse that has gripped German politics all week showed signs of breaking Friday as a main center-left party backed down from pledges that it would not consider teaming with Chancellor Angela Merkel to form a government.

The shift by the Social Democrats, or SPD, gives Merkel a potential path out of a crisis that’s been called the worst of her 12-year tenure. The political impasse has continued since national elections in September.

The change of heart by the center-left party also lessens the chance that Germans will go back to the polls in early 2018 after the inconclusive election left the country without an obvious formula for a stable government.

Merkel’s center-right Christian Democratic Union, or CDU, remains the dominant party, but still needs other parties to cobble together a governing partnership.

Since that September vote, the SPD has insisted it will go into opposition rather than form another so-called grand coalition with Merkel’s party.

That pledge was repeated as recently as Monday, after talks among the CDU, the probusiness Free Democrats, and the environmentalist Greens broke down. It left Merkel without negotiating partners as she seeks to extend her leadership of Germany to a fourth term.

But on Friday, after days of arm-twisting by German President Frank-Walter Steinmeier and a marathon eight-hour meeting of the party’s leadership, the SPD said for the first time that it’s ready to talk.

‘‘The SPD will not say no to discussions,’’ said party General Secretary Hubertus Heil.

That willingness does not mean Germany is headed for another grand coalition of the sort that has run the country for eight of the past 12 years.

Top party officials, including SPD leader Martin Schulz, are reported to adamantly oppose such an arrangement. They blame their position as Merkel’s junior partner for the party’s downward slide in the polls, including a September result that was its worst since World War II.

But the party is also reluctant to contest another election so soon after its September drubbing. And after the Free Democrats pulled out of talks for a so-called Jamaica coalition ­— the colors of the parties matched those of the island nation’s flag — a change of heart by the SPD appeared to be the only way for Germany to avoid another vote.

Schulz told reporters in Berlin on Friday that the talks ‘‘won’t automatically take a particular direction.’’

‘‘Should the talks mean that we participate in the formation of a government, in whichever form or constellation, then our party members will vote on it first,’’ he added. The coalition talks would probably take several weeks, and a ratification vote by party members could delay the formation of a new government even further.

Short of another grand coalition in which the SPD and the CDU govern together, the SPD could prop Merkel up by agreeing to support her government on a vote-by-vote basis. But Merkel said in a Monday night interview that she would prefer a new election to the uncertainty of a minority government.

The impasse has no direct precedent in Germany’s postwar political history.

It has stirred speculation over how long Merkel can hang on to the chancellorship, and whether a new vote might give even more impetus to the far-right Alternative for Germany party.

It has also spawned anxiety across Europe, where other governments are looking to Germany for leadership on the continent’s biggest challenges.

But markets have been relaxed about the turmoil. The euro has risen in recent days even as Europe’s most important economic and political player struggled with a level of uncertainty that is common elsewhere across the continent but is virtually unknown in Berlin.

Steinmeier, the president, has played a crucial role in recent days in steadying the country. Although his position is largely ceremonial, he has stepped in this week to prod the parties back to the negotiating table.

As a former SPD foreign minister, he has had particular influence with the Social Democrats. Germany’s oldest party has been badly divided over whether to enter talks.

Any deal with Merkel’s CDU is likely to involve weeks or perhaps even months of negotiation. It also could involve a change in leadership for the SPD, as Schulz has come under fire for ruling out talks for the past two months even as many in his party favored them.

Christian Ude, the former SPD mayor of Munich, said the party that has long represented the interests of German workers lacked ‘‘self-confidence’’ and direction, with no clarity about its goals.

‘‘I don’t think everyone should just be blaring out solutions into the world,’’ he told Deutschlandfunk radio on Friday. ‘‘Because that’ll just reinforce the image of an agitated heap of chickens.’’

German companies are watching the developments closely but appear to be confident a favorable solution will be found, according to surveys.