Emerging after five hours of talks, Horst Seehofer, leader of Bavaria's Christian Social Union (CSU), told reporters he would remain in his post after a deal with Ms Merkel's Christian Democrats (CDU) that he said would stem illegal immigration into the country.
Seehofer's move could possibly end the long-time political alliance between Merkel-Christian Democratic Union (CDU), making Germany's ruling coalition lose parliamentary majority and throwing the country into deeper political crisis.
Germany's constitution prevents federal ministers from outright quitting their positions, and must request to be dismissed by the German President.
Sources said Seehofer rejected Merkel's assessment that the EU-wide measures would "have the same effect" as his demand to turn away at the border asylum-seekers already registered in other European Union nations.
"I would like to make a promise to you: the Austrian presidency will do everything possible so that in the long term we have a Europe without internal borders again", Kurz told MEPs.
The deal also faces a potential challenge from the European Union.
Seehofer and Merkel are in a dispute over Germany's asylum policy.
Rome's hardline Interior Minister Matteo Salvini has stressed that his overburdened country is not ready to take in any more migrants.
While Seehofer's comparatively strong stance has caused this clash with Merkel, the Bavarian leader remains a centre-right figure fundamentally unopposed to mass migration, and the new compromise will do nothing to undo the effects of decades of mass migration to Germany - most dramatically those million-plus arrivals who walked through Europe during the migrant crisis. Last week, an FG Wahlen survey said 91% favour European solutions on migration, an endorsement of Merkel's line and a snub to Bavaria's nationalist push for unilateral border measures.
Bavaria's Interior Minister Joachim Herrmann, who has been tipped as a potential successor to Mr. Seehofer, said in a radio interview his party wanted an agreement with the CDU but gave no indication about what a compromise could look like. Representatives of the three elements of the coalition, the CDU, CSU and SDP are meeting to discuss the agreement.
She could also call a vote of no confidence.
While she still has CDU backing, Merkel is safe.
What is 100 percent clear is that nobody wants new elections because only ...
Merkel, who has been in power for 13 years, is suddenly reversing her immigration policy in the hopes of keeping her government together, according to new reports.
That decision convulsed European politics, fueling the rise of anti-immigration parties including the far-right Alternative for Germany (AfD) party, which now threatens to unseat the CSU in October's regional elections.