"After intensive discussions between the CDU and CSU we have reached an agreement on how we can in future prevent illegal immigration on the border between Germany and Austria", Mr Seehofer told reporters as he was leaving the CDU's Berlin headquarters.
The coalition parties, comprising Merkel's Christian Democrats (CDU), the CSU and Social Democrats (SPD), are holding a series of meetings on Monday to decide what action to take.
Officials, he said, must also block refugees if they have already registered in another European country.
Merkel, who has long favored open borders between European countries, agreed to allow "transit centers" along the Austrian border for the objective of screening asylum seekers.
Alternatively it could break up the two parties' seven-decade-long partnership, depriving Merkel of her majority in parliament and pitching Germany into uncharted political waters.
The proposal could also shift the political crisis south to Austria, where the government said it could take its own measures to protect its borders.
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Seehofer, a long-time Merkel critic, had openly challenged her with a plan to order border police to unilaterally shutter German border crossings with Austria to many asylum seekers, effectively daring the chancellor to fire him.
The CSU softened its stance in the face of withering criticism across party lines and poor polling results, insisting that the alliance with the CDU must live on.
Germany recorded just 18,349 people this year who would be eligible for deportation to other European Union states under the proposed scheme.
At the national level, Merkel proposes that migrants arriving in Germany who first registered in another European Union country should be placed in special "admission centres" under restrictive conditions, according to a document she sent to the CSU and SPD.
Mrs Merkel got backing from both parties at a parliamentary meeting on Monday.
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Some Social Democrats accuse the CSU of wanting to appear tough on immigration before a regional election in Bavaria in October where the conservatives are expected to lose voters to the anti-immigrant party Alternative for Germany.
The "Free State" with its beer-and-lederhosen Alpine traditions, powerful industries and impenetrable dialect has a more conservative bent than other German regions.
They argued such zones would not limit the number of migrants given that most were fleeing wars in the Middle East and Afghanistan and therefore entitled to asylum in Germany.
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.
However, Seehofer agreed to see Merkel on Monday before making a final decision.
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