One possibility is for the 70-year-old CDU and CSU alliance to split which would rob Merkel of her parliamentary majority.
Merkel, who has become the key advocate of lax border control in Europe, was opposed to the plans, insisting a European-wide solution was needed to address the problem.
After a meeting with Seehofer on Saturday evening, Merkel told the German broadcaster ZDF on Sunday that the two people's meeting had "pretty good results", and she hoped to further work with her political ally CSU.
Ahead of a hard Bavarian state election in October, the CSU is determined to show that it is tough on migration.
"We have reached an agreement after very intense negotiations", Seehofer agreed, stressing that he meant to stay on in his cabinet post after earlier threatening to quit and gloating that "it's worth fighting for your convictions". Seehofer did not comment on that during his brief statement to journalists after his party's meeting.
"I won't let myself be fired by a chancellor who is only chancellor because of me", he was quoted as saying in an apparent reference to the CSU's traditionally strong election results in Bavaria. The pair hit yesterday's low at 1.15900 during late North American market hours but recovered uptrend movement post news update from Germany.
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However, the more conservative CSU - which has sparred with Merkel over migrant policy on and off since 2015 - believes its credibility is at stake as it tries to curb support for the anti-migration Alternative for Germany party in the upcoming Bavaria election. She also would not speculate on whether she might fire him or if the issue could lead to a government confidence vote in parliament.
Merkel says a plan to regulate immigration that European Union leaders approved Friday and bilateral agreements in principle that she hashed out with some countries for them to take back migrants would accomplish what Seehofer seeks. "And what has now been agreed is really a clear agreement that is very sustainable for the future".
"The CSU's risky ego trip is paralyzing Germany and Europe", SPD chairwoman Andrea Nahles told journalists in Berlin.
He said that "there is an abundance of possibilities. for compromises", but didn't specify what they were.
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. "So I think action in Germany to strengthen European interests is absolutely necessary".
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.
A coalition of the Social Democrats, the Christian Democrats and the CSU must accept the new accord before it can go into affect.