A rift in the German government over mass migration showed no sign of resolution on Sunday evening as leaders of Chancellor Angela Merkel's party and its coalition partner met separately, each apparently waiting for the other to blink.
If the CSU were to withdraw its support for Ms. Merkel's party, her options would include joining forces with the migration-friendly Greens or heading a minority government.
Merkel said arrivals had dropped by 20% in the first five months of the year compared with the same period in 2017.
German Chancellor Angela Merkel has reportedly secured agreements with 14 European Union countries to facilitate the rapid return of migrants who have been rejected for asylum.
Officials from the Bavaria-based CSU accused Merkel of rejecting several compromise proposals made by Seehofer to heal the rift with her own CDU.
She said she would wait to see what the leadership of the two parties decides "and then we will see what comes next, step for step". The CDU's leaders, who are now gathered in Berlin for a second straight day of discussions, said they still see room for a compromise solution in the migration dispute.
Merkel had set off for a European Union migrant summit in Brussels last week to fight for a deal that would appease her hardline allies, preserve her already unstable governing coalition and defend an embattled European Union.
He said that "there is an abundance of possibilities ... for compromises", but didn't specify what they were.
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It reported that Alexander Dobrindt, the leader of the CSU in parliament, told others Mr Seehofer could not be allowed to resign.
The interior minister's "master plan", which triggered the present German government crisis just over two weeks ago, would see asylum-seekers who had already been registered elsewhere being shut out of Germany - a potential breach of European Union law and the Geneva Convention on refugees' rights.
"I said that I would vacate both my offices (as federal interior minister and CSU party chief) in the next three days", Seehofer told reporters in Munich after talks with his party stretching into the small hours.
"The blame game between CDU and CSU must end, because it is irresponsible", she said. That would likely end the seven-decade partnership of the CDU and CSU, which have a joint parliamentary group, and in turn would leave the government just short of a majority. Seehofer had initially proposed an immediate rejection of immigrants who have been registered in other European Union countries but later agreed to a phased implementation of the plan, contradicting Merkel's stance on the matter.
CSU leaders are divided over how to face down a challenge from the anti-immigration Alternative for Germany (AfD) in October's regional election.
"They need to get their act together", Daniel Guenther, the CDU premier of Schlewsig-Holstein state, said of the Bavarian party on ARD television.
Its success was based on strident anti-immigration rhetoric, attacking Mrs Merkel's decision to let in more than a million asylum seekers in 2015-2016.
The EU and bilateral deals were "only possible because the chancellor enjoys respect and authority throughout Europe", Germany's EU Commissioner and CDU politician Guenther Oettinger said in an interview with the Frankfurter Allgemeine Sonntagszeitung weekly.