BERLIN—German Chancellor Angela Merkel secured a two-week reprieve in her confrontation with her coalition partner, averting at least for now a collapse of her government over migrants.

Ms. Merkel clashed with longstanding ally Horst Seehofer, interior minister and chairman of the Bavarian sister party to her conservative bloc, last week after he threatened to go ahead with a plan she vetoed to start turning back some migrants at the German border.

After...