On Monday, reports emerged that Seehofer has agreed to give Merkel two weeks to come up with a solution, but the situation is still highly concerning for investors already anxious about politics in the European region.
Merkel is seeking a consensus on the issue from neighboring countries.
"We see somewhat positive developments there", Merkel told reporters Tuesday.
Germany's interior minister is insisting that his party has no intention of bringing down Chancellor Angela Merkel and her government, but there's no sign yet of a compromise in a bitter standoff over migration.
Merkel has said she is "favourable" to a French call to create a European Intervention Initiative of forces which could be deployed rapidly to deal with crises outside the framework of North Atlantic Treaty Organisation.
She said yesterday that she supports 62 of his 63 points.
Now, Bavaria's conservative Christian Social Union (CSU), which has been in alliance with Merkel's Christian Democrats for decades, wants Germany to turn away some refugees at the country's border.
"Our goal remains a European answer to these challenges", she said.
That hope, however, is running up against an "axis of the willing" to combat immigration announced last week by Italy's new far-right interior minister and his German and Austrian counterparts.
US President Donald Trump on Monday blamed migrants in Europe for what he inaccurately described as a rise in crime in Germany and for violently changing the culture, adding that what was happening with immigration there presented a similar threats to the United States.
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A populist-far right government in place in Italy, as well as the conservative-far right in power in neighbouring Austria, have also taken an uncompromising stance on immigration.
While she has rejected unilateral action to turn back some migrants at the German border, Merkel has raised the possibility of forging agreements between two or more countries if an EU-wide asylum deal can't be reached.
Italian Interior Minister Matteo Salvini, who this month refused entry for a boat with 600 refugees, on Saturday said on his Facebook page the country won't permit two ships allegedly carrying migrants and asylum seekers from Libya to reach its shores.
Germany had the most asylum seekers of any European nation, with more than 200,000.
Top CSU leaders huddled Monday morning in the party's home base of Munich.
Though arrival numbers have always been decreasing and are now low, migration has shot back to the top of Europe's political agenda also because German Chancellor Angela Merkel's coalition partner issued an ultimatum for an EU-wide deal on migration.
The interior minister now wants to turn away at the border new arrivals who have previously been registered in another European Union country - often their first port of call, Italy or Greece.
The joint cabinet meeting with France offers Merkel a chance to air proposals for revamping regional asylum policy ahead of a European Council meeting June 28-29.
Merkel must now attempt to forge a deal by an EU summit on Thursday and Friday next week, and report back to her Christian Democratic Union on July 1.
NELSON: The interior minister and his party, which is facing a major challenge from far-right populists in upcoming regional elections, say they will unilaterally prevent migrants from crossing Bavaria's global borders if Berlin doesn't act. Seehofer is chairman of the CSU.