Seehofer offered to quit as interior minister and as leader of the Christian Social Union (CSU), the Bavarian sister party of Merkel's Christian Democrats (CDU), during a marathon party meeting Sunday, but was later persuaded by CSU colleagues to meet with Merkel one more time and attempt to resolve the row, Reuters reported.
"That is a decision that I cannot accept", Alexander Dobrindt said, according to sources from Sunday's high-level party meeting.
Seehofer, whose party faces a state election in the fall, has threatened to turn away at the borders migrants whose asylum requests Germany already rejected or who already sought asylum elsewhere in Europe.
Facing a state election in October, the Bavaria-only CSU hopes to win back votes eroded by the anti-migration Alternative fuer Deutschland and prevent the bordering state from being further impacted by migration. If Seehofer goes ahead with his policies, the dispute could end the decades-old conservative alliance between the CSU and Merkel's CDU.
The leadership of Merkel's party on Sunday night approved a resolution stating that "turning people back unilaterally would be the wrong signal to our European partners". The German leader would not comment Sunday on the outcome of the talks.
As the CDU and CSU parties hunkered down in Berlin and Munich, a compromise appeared ever more elusive.
The CSU exists only in Bavaria, the CDU in Germany's 15 other states.
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So we deserved to be eliminated. "We didn't deserve to win the title again and we didn't deserve to progress to the round of 16". The German players trudged off goalless at halftime, with frowns on faces and whistles ringing out from the terraces.
Should the government break down completely, it could pave the way for new elections, an option that Merkel has previously said she prefers to ruling in a minority government.
Merkel's government has been pushed to the brink over the migration issue after allowing more than one million asylum-seekers into Germany since 2015.
"The sum total of everything we've agreed on is the same as what the CSU wants", the chancellor told broadcaster ZDF the next day.
The source of the impasse is a migration plan hatched by Seehofer to take unilateral action to turn back migrants who have been registered first in another European Union country.
German Chancellor Angela Merkel gestures as she attends a press conference after the board meeting of Germany's Christian Democratic Union (CDU) in Berlin, Germany, June 18, 2018.
She confirmed that she had clinched bilateral agreements with Spain and Greece to handle migrants who make their way from southern Europe north to Germany, but did not have a similar deal with Italy.
Nevertheless, the anti-refugee, anti-Islam Alternative for Germany (AfD) surged into federal parliament for the first time previous year, leading to months of paralysis while Merkel struggled to put together a workable coalition.
Weeks of "Merkel-bashing", however, have failed to help the CSU, as a Forsa poll last week showed around 68 percent of Bavarians backed Merkel's quest for a Europe-wide answer to migration rather than Germany going it alone.