"We just want to finally have a sustainable solution to send refugees back to the borders".
Seehofer's "migration master plan", which Merkel last week refused to endorse, would see asylum seekers arriving at Germany's borders turned away if they have no identification papers, have already had an asylum claim rejected in Germany, or are already registered in another country in the EU - proposals that rights group say contravene European and worldwide agreements.
The chancellor, who is scheduled to meet her French counterpart Emmanuel Macron next week, said Germany and France would seek to set the agenda for European Union cooperation on defense, security and foreign policy ahead of the June summit.
The move sparked a clash between France and Italy as immigration also triggered a domestic crisis for Merkel, a leader already weakened by her decision in 2015 to keep open German borders to a mass influx of more than one million refugees.
Merkel's woes come as European Union countries are once again at loggerheads over immigration, triggered by Italy's refusal this month to allow a rescue ship carrying 630 migrants to dock. Polls show Merkel and her coalition enjoy broad support among voters. Seehofer - then the governor of Bavaria, where most migrants first entered Germany - became a leading critic of her welcoming approach. But Seehofer's party faces a crucial election in October, and it is determined to toughen its stance on migration, faced with the growing popularity of the anti-immigrant, populist party Alternative for Germany.
The Christian Democratic Union (CDU) politician said it was still unclear in Berlin what the essence of the disagreement between the Chancellor and Mr Seehofer was and that other members of the coalition had been left "in the blue".
Seehofer last week defied Merkel to announce a tough new immigration policy that would see some asylum seekers turned away at the borders of Germany.
CSU leaders insisted that the causes for the drop in support were in Berlin and that Germany's migration policy was a major factor.
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President Trump is digging in on a demonstrably false claim that the crime rate in Germany has risen as a result of refugees in that country, despite the fact that the government of Germany recently released data showing the exact opposite - that the crime rate has actually decreased in Germany to the lowest levels since 1992.
Merkel would still have options if the CSU quit the coalition: Greens leader Annalena Baerbock refused on Monday to rule out replacing the CSU in Merkel's coalition.
Seehofer and Merkel have long had an awkward relationship.
"Turning away migrants at our borders at the heart of Europe will lead to negative domino effects that could hurt Germany, and put into question European unity", she warned.
Commenting on the supposed deadline for Merkel to negotiate an EU-wide solution, Seehofer said that "the whole issue is not about these 14 days but about fundamental differences" between the leadership of the two sister parties.
If Seehofer decides to go it alone, Merkel would have to fire him, sparking an unprecedented CDU-CSU split, political scientist Heinrich Oberreuter told business daily Handelsblatt.