In an earlier series of closed-door talks, Seehofer was also said to have muttered, twice, that he "can't work with this woman anymore", though the leaked complaint was later denied by his CSU party.
Angela Merkel's face-saving deal with her conservative allies in Bavaria shows how indispensable the chancellor is to her party - even if she is weakened.
"We now have a clear agreement how to prevent illegal immigration across the Austrian-German border in future", said Seehofer, whose CSU is the traditional Bavaria state ally of Merkel's CDU party.
Horst Seehofer, both interior minister and leader of Bavaria's Christian Social Union (CSU), deemed plans that Merkel brought back from an EU summit last week as too little to stop him introducing new national border controls.
Merkel, however, rejected a key provision: turning back at the border all migrants previously registered in another European Union country as a unilateral act that would come at the expense of other member states. But Merkel had refused saying there needed to be other European nations involved.
"We discussed common solutions to fight clandestine immigration between one European Union country and another and the protection of Europe's exterior borders", Salvini said in a statement.
Ms. Merkel, anxious about European Union unity, opposes such a unilateral move without agreements between Germany and its neighbors.
But instead he and Ms Merkel have agreed on setting up detention centres on Germany's border with Austria that will process immigrants and return them if necessary.
In a meeting with his party leaders on Sunday night, Seehofer offered to resign from his ministerial role and party leadership, reports said.
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Alternatively, it could break up the two parties' 70-year partnership, depriving Merkel of her majority in parliament and pitching Germany into uncharted political waters.
Merkel has not resolved the underlying tensions in her coalition.
Merkel has faced a strong backlash, and been weakened at the polls, over her 2015 decision to keep open German borders to a mass influx of migrants, many from war-torn Syria, Iraq and Afghanistan, that led to more than one million arrivals.
Rome's hardline Interior Minister Matteo Salvini has stressed that his overburdened country is not ready to take in any more migrants.
The centre-left Social Democrats, another partner in the coalition, must also accept the deal along with neighbouring Austria.
In an extremely fluid situation, Merkel and Seehofer are due to meet later in the day and before that, a joint session of the parliamentary groups of the CSU and CDU is due to take place, although there was some doubt if it would go ahead. "And as a result we will see a crash - damaging both parties." .
"And then Chancellor Merkel is entitled to dismiss her minister of interior".
Three years on, the centre-left SPD, wary of fresh elections, may feel less inclined to provoke a new crisis, but it could again reject the proposal at a meeting with members of Merkel's bloc in Berlin on Tuesday.