The dpa news agency reported Saturday Merkel also informed government coalition partners in a letter she wants "anchor centres" to process migrants at Germany's borders.
Seehofer said he was ready to step down as minister and as chair of his Christian Social Union (CSU) at a meeting where his party's leadership was discussing whether to accept immigration proposals Merkel brought back from Brussels last week. The CSU is facing a state election in Bavaria in October, and has opted to take a hard-line anti-immigration stance as its main campaign strategy.
Seehofer had previously warned that, unless Merkel came up with a satisfactory EU-wide solution to dealing with migrants, he would use his power to make sure that asylum-seekers who applied for asylum in states other than those where they'd first entered, would be turned away at the border.
Under the EU's Dublin convention, largely honoured in the breach since Merkel's 2015 decision to open Germany's borders, asylum seekers must lodge their requests in the first European Union country they set foot in.
Volker Bouffier, premier of the state of Hessen and Merkel's close ally, said that the CSU should be pleased at what it had achieved so far as he arrived at a similarly protracted meeting of his and Merkel's CDU in Berlin.
Austrian GP: Verstappen ran with 'cut' Red Bull floor in practice
Verstappen relished it all at the front of the field as he managed his tires and cruised to victory at the Red Bull Ring . With temperatures much higher than at any other point across the weekend, the tires were suffering badly.
"The sum total of everything we have agreed upon has the same effect" as what Mr Seehofer has demanded, Ms Merkel said in an interview with ZDF television.
Under the deal brokered in Brussels, EU leaders agreed to consider setting up "disembarkation platforms" outside the bloc, most likely in North Africa, in a bid to discourage migrants and refugees boarding EU-bound boats.
"We want to continue to reduce the number of migrants coming to Germany", she said.
Germany's interior minister has offered his resignation after a conflict with Angela Merkel over migration policy, party figures say.
Seehofer wants the right to turn back at Germany's borders asylum seekers already registered in another European Union country.
Top French criminal Redoine Faid escapes prison by helicopter
Rédoine Faïd abandoned the helicopter on the outskirts of Paris after using it to escape Réau prison in the south-eastern suburbs. The ministry said Redoine Faid's escape only took "a few minutes" Sunday and no one was injured or taken hostage.
The source of the impasse is a migration plan hatched by Seehofer to take unilateral action to turn back migrants who have been registered first in another European Union country.
According to a document sent to coalition partners, Merkel sought to assauge the hardliners with deals with 16 other countries to return already-registered migrants if they reached Germany.
The governing coalition - which would then consist only of the CDU and Social Democrats (SPD) - would be short of a majority and Merkel would either have to rule with a minority government or seek the formal support of the Green Party or the pro-business FDP.
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.
Angela Merkel, German chancellor and chairwomen of the German Christian Democratic party (CDU), sits in her auto as she leaves after the recording of a TV interview in Berlin, Germany, Sunday, July 1, 2018.
Germany eliminated with shocking loss to South Korea
The normally rock solid Neuer spilled a free kick in the first half but his counterpart, Jo Hyeon-woo, didn't put a foot wrong. But this is the third straight World Cup in which the previous champion has been knocked out before the end rounds.
Over recent days, speculation had focused on the possibility of Merkel firing Seehofer if he went ahead unilaterally with his plan.