BERLIN—Germany’s hope of breaking a streak of more than 100 days without a government is now riding on repairing a broken political marriage.

On Sunday German Chancellor Angela Merkel began a last-ditch effort to form a government by beginning five days of talks with her former governing partner, the Social Democrats. The center-left party had previously vowed not to work with Ms. Merkel’s conservative bloc this time around in another so-called grand coalition of Germany’s two centrist parties.

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