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.
However, criticism from Vienna and her junior coalition partners, the Social Democrats (SPD), threatened to throw a spanner in the works.
Germany's constitution prevents federal ministers from outright quitting their positions, and must request to be dismissed by the German President.
They have agreed to a plan for so-called transit centres, from which people who have sought asylum in a different European Union country can be sent back to their arrival point, if the other state agrees.
In cases where no such bilateral agreements exist, the asylum seekers would be sent back across the border "on the basis of an agreement with Austria" that was to be negotiated, it said.
As Merkel won key concessions from European Union partners on toughening migration rules, Seehofer and the CSU faced increasing pressure from other parties to avert a historic coalition breakdown.
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.
He could defy her orders by ordering border police to carry out his plan, which would force her to fire him and nearly certainly break up the CDU-CSU alliance, or he could accept a humiliating climbdown or resign.
Last weekend's marathon Brussels talks in search of a "European solution" and the meetings between Merkel and Seehofer that followed have cast considerable doubt over that trifecta.
As the CDU and CSU parties hunkered down in Berlin and Munich, leaders on both sides sought to clarify what was a stake.
Germany's political crisis is the latest sign of a growing divide across the European Union between those who want to maintain open borders and those who want to restrict the number of migrants entering the bloc.
Speaking of the deal after terse negotiations on Monday, Mrs Merkel said: "We want on the one hand to set up transit centres in Germany and from there carry out returns in agreement with countries from which asylum seekers come and where they are already registered". But a Forsa poll on Tuesday showed a majority of Germans to be unhappy about the agreement.
German Chancellor Angela Merkel has been criticized for adopting a much too relaxed policy on immigration.
The strongest voice in opposition to mass migration in the Bundestag is the Alternative for Germany (AfD) party, who have 94 seats to the governing coalition's 246.
Nevertheless, the anti-refugee, anti-Islam Alternative for Germany (AfD) was propelled into federal parliament for the first time previous year by outrage over immigration, leading to months of paralysis while Merkel struggled to put together a workable coalition.
However, Seehofer agreed to see Merkel on Monday before making a final decision.