Mr Seehofer leads the Christian Social Union (CSU), the Bavarian sister party of Mrs Merkel's Christian Democrats (CDU). In a meeting with his party leaders on Sunday night, Seehofer offered to resign from his ministerial role and party leadership, reports said.
Issues among the C.D.U. were precipitated by the surprising strength of the Alternative for Germany political party in the country's 2017 elections, which won 94 seats in the Bundestag after previously being unrepresented.
In the first five months of this year, roughly 4,600 "unauthorised entries" were recorded at Germany's border with Austria, according to the German police. They will be returned to whichever European Union country they first registered, provided Germany has a bilateral agreement with that country to return asylum seekers. However, sources said senior party officials were trying to convince him to stay in his post.
One day into the job he caused a headline-grabbing stir by declaring that "Islam is not part of Germany", contradicting Merkel and rekindling a divisive debate about cultural identity.
It is unclear what effect Seehofer's resignation as interior minister and CSU leader, if he goes through with it, would have on the alliance between the two conservative parties and their governing coalition with the center-left Social Democrats. They would either be sent back to European Union countries that previously registered them or, in case arrival countries reject this, be sent back to Austria, pending a now questionable agreement with Vienna. If not, the rejected applicants are expected to be returned to Austria, although the two countries have yet to negotiate this.
Jens Spahn, an arch critic of Merkel's migrant policy, may be unpalatable to many in the CDU, especially after making some controversial comments on poverty and being photographed with the new, outspoken US ambassador, a defender of US President Donald Trump.
Politics professor at Berlin's Hertie School of Governance Andrea Rommele said of the move, "It was a kind of open declaration of war against Ms. Merkel". No details emerged, but the expectation is that the CSU will support Merkel after its executive committee convenes on Sunday.
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.
In Monday's deal, both sides agreed to set up closed "transit centres" - similar to existing facilities at airports - that would allow German authorities to speedily process applicants.
Rome's hardline Interior Minister Matteo Salvini has stressed that his overburdened country is not ready to take in any more migrants. He insisted the CSU doesn't want to break up the conservative partnership.
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