A almost eight-hour meeting of the CSU in Munich was put on hold after the party's leader, Interior Minister Horst Seehofer, made his offer to resign both from Merkel's Cabinet and as head of the CSU.
The conservative Bavarian Christian Social Union (CSU) is a coalition partner of Angela Merkel's centre-right Christian Democratic Union (CDU) in Berlin. But earlier, Bavaria's premier Markus Soeder, mindful of October regional elections in which he faces a stiff challenge from the anti-immigration Alternative for Germany (AfD), was positive.
Last week he threatened to turn asylum seekers away from Germany's borders unless Mrs Merkel reached an acceptable deal with other European Union partners.
Mr Seehofer, one of Mrs Merkel's biggest political rivals, also said the matter was affecting the "credibility" of his role as party leader, hinting at a possible resignation.
They follow European Union leaders agreeing to consider setting up "disembarkation platforms" outside the European Union, most likely in North Africa, in a bid to discourage migrants and refugees boarding EU-bound smuggler boats. Party leader Andrea Nahles said that "the CSU is on a risky ego trip that is paralyzing Germany and Europe".
Following nine-hour marathon talks at a two-day European Union summit, Mrs Merkel thought she had secured a deal and tried to put a positive spin on the result saying it was a good signal that leaders had been able to agree a common text on the controversial migration issue.
Though the master plan remains unpublished, it emerged on Sunday evening that Seehofer had handed it out at the CSU meeting, though it had not been made available to the CDU leadership in Berlin.
Merkel's CDU relies on CSU to maintain power through a coalition, also including the Social Democrats (SPD), formed three months ago after an election in September.
LeBron James Inks A $154M Deal With The Los Angeles Lakers
James had been linked to several franchises, with the Philadelphia 76ers and Houston Rockets reportedly in the running. Cleveland has lost to Golden State in the finals each of the last two years, and in three of the last four.
Actress brings along her boyfriend to Akash Ambani's pre-engagement bash
But the one that has got everyone hooked to their mobile phones is Nita Ambani's elegant classical style dance performance. In the video, Isha is seen welcoming Shloka as a popular Gujarato track played in the background.
Betting site offers odds on Drake dissing Pusha T on new album
Static Major and Ty Dolla $ign are both on "After Dark". Drake revealed nothing about the song's genesis. Check out the album in full below.
Member countries could also create processing centres to determine whether the new arrivals are returned home as economic migrants or admitted as refugees in willing states.
But right-wing governments in Hungary and Poland have since said they have not reached any new deals on asylum.
Differences with the CSU only pertained to the way how to achieve a reduction in migration, not to the goal as such, Merkel said.
Merkel is hoping a deal secured in Brussels earlier this week will placate her Bavarian allies, who are demanding a significant hardening of Germany's immigration policy.
Merkel's decision in 2015 to open doors for refugees fleeing conflicts and persecution was widely criticized by conservative media outlets, and was exploited by the far-right and populist parties.
Nevertheless, the anti-refugee, anti-Islam Alternative for Germany (AfD) was propelled into federal parliament for the first time past year by outrage over immigration, leading to months of paralysis while Merkel struggled to put together a workable coalition.
Ahead of a hard Bavarian state election in October, the CSU is determined to show it is tough on migration.