Merkel's center-right Christian Democratic Union (CDU) remains the dominant party, but it still needs to work with other parties to cobble together a governing partnership.
Since the September vote, the center-left Social Democrats (SPD) have insisted they will go into opposition rather than form another "grand coalition" with the CDU.
That pledge was repeated as recently as Monday after talks broke down among the CDU, the pro-business Free Democrats and the environmentalist Greens. This left Merkel without negotiating partners as she seeks to extend her leadership of Germany to a fourth term.
But Friday, after days of arm-twisting by President Frank-Walter Steinmeier and a marathon eight-hour meeting of the party's leadership, the SPD said for the first time that it is 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.
Later Friday, Schulz said the party was shifting its stance due to "its responsibility to the country." He said any agreement to back Merkel will be subject to a vote from the party's membership, which has been highly skeptical of the idea.
Short of another grand coalition in which the SPD and the CDU govern together, the SPD also could prop up Merkel by agreeing to support her government on a vote-by-vote basis. But Merkel had said in a Monday night interview that she would prefer a new election to the uncertainty of a minority government.
This week's 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 also has 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.
Steinmeier is expected to convene a meeting next week between Merkel and Schulz.
Any deal 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 Friday, "because that'll just reinforce the image of an agitated heap of chickens."
Luisa Beck contributed to this report.