Indications of a shift came when SPD General Secretary Hubertus Heil told reporters late Thursday that the party "is convinced that discussions must be held. the SPD will not rule out talks".
President Frank-Walter Steinmeier's office said that Mrs Merkel, the head of her party's Bavaria-only Christian Social Union, Horst Seehofer, and Social Democrat leader Martin Schulz have been asked to come together next week to discuss teaming up in another "grand coalition" - the configuration now governing Germany.
"After meeting this week with the leaders of the CDU, CSU and SPD the federal president has agreed to meet a joint meeting at Schloss Bellevue", Steinmeier's spokeswoman said in a statement.
His cautious language was echoed on Friday morning by SPD deputy leader Manuela Schwesig, who said that a new coalition government was no certainty. Failure to produce a coalition would be a first in the history of the federal republic.
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The couple have been dating since May a year ago , and made their first public appearance together in September. The public could also expect an official proclamation of their engagement by the new year.
Merkel's CDU/CSU was the largest bloc after federal elections on September 24, but it failed to secure an absolute majority in parliament.
After Martin Schulz, the SPD's leader, ruled out another grand coalition - citing the need to rebuild his party and an unwillingness to leave the far-right Alternative for Germany as the largest opposition group in Parliament - few viable coalition options remained.
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The turnabout by the centre-left party, which had said it would go into opposition after suffering its worst result in 70 years in a September election, could help avert a disruptive repeat election in Europe's economic and political powerhouse.
Schulz himself had seemed to reassess his stance by Wednesday when he said he was "fully aware of its responsibility in the current hard situation", before adding "I'm sure we will find a good solution for our country in the coming days and weeks". A cartoon published by Cicero magazine on Friday depicted the SPD as a mouse being enticed out of its hole by a waiting feline Merkel.
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He went on to assert that "this government does not stop dividing the Jewish people in Israel and overseas ". "Israel and the U.S. are countries that have very different daily lives".
"It is not the SPD that is responsible for this situation", he said.