Seehofer reportedly argues that measures to tackle migration agreed at a European Union summit last week aren't enough.
After half a year of coalition building, Seehofer, having been ousted by ambitious rival Markus Soeder as Bavarian state premier, returned to Berlin, where he previously held ministerial posts, to rejoin Merkel's cabinet.
If Seehofer does quit, the CSU could offer a replacement interior minister if it aims to remain tied to Merkel's CDU party. "Because we are a success story for Germany".
"This provides a break, but it's not the end of the infighting", said Carsten Nickel, an analyst at Teneo Intelligence in London.
In this file photo taken on April 14, 2016, German Chancellor Angela Merkel (L) and then Bavarian state premier and leader of the conservative Christian Social Union (CSU) Horst Seehofer give a press conference at the Chancellery in Berlin.
If the agreement reached is approved by the German government as a whole, "we will be obliged to take measures to avoid disadvantages for Austria and its people", Vienna's rightwing government warned. But her unilateral 2015 decision to open Germany's borders to a million refugees from Africa and the Middle East spurred the rise of the far-right Alternative for Germany, presenting the CSU with a political opponent to its right for the first time ever. "With this the very spirit of partnership in the European Union is protected and at the same time, it is a decisive step towards organizing and managing secondary migration", Merkel said.
Merkel's Christian Democratic Union (CDU) passed a resolution on Sunday night supporting her position on migration.
Meanwhile, the SPD said they would be meeting to discuss whether the compromise between the two conservative parties was acceptable to them.More news: Dude, Dell is going public again
The proposal could also shift the political crisis south to Austria, where the government said it could take its own measures to protect its borders. "That's something we've painfully missed in recent weeks". And if he doesn't keep with this promise the CSU will lose all of its credibility.
Image copyright Getty Images Image caption Passau in Bavaria was on the frontline of Europe's 2015 migrant crisis How did the events unfold?
A Forsa poll published Monday showed some 77% of respondents said the conflict over immigration was putting the stability of the government at risk and two thirds said the CSU's behavior wasn't responsible.
The last-minute compromise capped an unprecedented challenge to Ms. Merkel's authority after she vetoed the interior minister's plan to turn back refugees at the border, and he countered that he would go ahead with it anyway.
But that would be dependent on guaranteeing sufficient protection for the EU's external borders, he said.
It was reported that Merkel had believed that the European solution could satisfy CSU's ultimatum, which was due on Sunday, otherwise Seehofer would bypass Merkel to implement a tougher asylum policy.
"The cost of getting to this deal ended up being much higher than the benefit of the actual outcome", she said.