But CSU parliamentary group chief Alexander Dobrindt "does not want to accept Seehofer's resignation", participants in the hours-long huddle said.
German media is reporting that the Christian Democratic Union (CDU), Merkel's main party, is deeply troubled by the news, and is looking to hold an internal vote on the matter, but will continue ahead with the migration pacts made thus far, and will continue to puruse deals with other EU partners.
Austrian Chancellor Sebastian Kurz and Interior Minister Herbert Kickl attend a news conference in Vienna, Austria July 3, 2018. The challenge from the Christian Social Union (CSU), which has functioned as the Bavarian wing of Ms. Merkel's Christian Democratic Union (CDU) since the founding of the Federal Republic, was unprecedented in its ferocity.
Austria's government has warned it could "take measures to protect" its borders after Germany planned restrictions on the entry of migrants as part of a deal to avert a political crisis in Berlin.
Merkel, who has long favored open borders between European countries, agreed to allow "transit centers" along the Austrian border for the goal of screening asylum seekers.
Merkel told journalists after the meeting that they had reached a deal and will create transit centres in the country from which migrants will be returned to countries they were in earlier.
The CSU party boss and now the head of Germany's newly christened interior and homeland ministry has deemed inadequate the European Union deals reached by Merkel allowing the return of some asylum seekers.
Officials, he said, must also block refugees if they have already registered in another European country. Seehofer wants to unilaterally turn back refugees already registered in other European Union (EU) member states, while Merkel opposes it and has been calling for a European solution.
That left him with only three options.
The CSU softened its stance in the face of withering criticism across party lines and poor polling results, insisting that the alliance with the CDU must live on.
However, the more conservative CSU believes its credibility is at stake as it tries to curb support for the rival anti-migration Alternative for Germany party in the Bavarian election.
Meanwhile for Merkel's troops, "the image of the country, our ability to act and our ability to govern" were at stake, said economy minister and close Merkel ally Peter Altmaier. "A majority of Germans back the chancellor".
But the CSU and CDU together form a center-right force that has dominated national politics for decades.
Since then, more than one million people have arrived in Germany, while Merkel's governments have repeatedly tightened immigration and asylum laws.
It was a spectacular turnabout for a leader who has been seen as the standard-bearer of the liberal European order but who has come under intense pressure at home from the far right and from conservatives in her governing coalition over her migration policy.
Opinion polls point to the AfD making a similarly spectacular entrance to Bavaria's regional parliament in October.
Seehofer told party colleagues at an executive committee meeting on Sunday that discussions with Merkel had been fruitless, according to a party source.