But the chancellor's pledge has been met with skepticism by some CSU politicians, who question the possibility of reaching an EU-wide agreement after several years of failed attempts.
However, Seehofer on Monday said he would only implement the policy if Merkel failed to reach a deal with other European Union states at the summit - effectively giving her two weeks to find a fix. The CSU lost thousands of voters to the far-right Alternative for Germany (AfD) party in federal elections previous year, and is fearful of further losses.
A CSU leadership meeting Monday in Munich unanimously backed Seehofer's plan to give Merkel until the end of the month to find a solution with other European Union countries.
At a meeting of the CSU leadership in Munich, the Bavarian party agreed to push for a policy on turning away migrants who had earlier been banned from Germany to be implemented immediately, but postponed until after an European Union summit at the end of June a ban on the previously registered, officials said.
Ahead of the CSU meeting, Bavaria's state premier Markus Soeder said the CSU wanted to back Seehofer's plan, but leave it up to the interior minister to decide how to implement it. Migration is "a European challenge that requires a European answer", Merkel said in her weekly podcast released Saturday.
If he actually does so unilaterally in defiance of the chancellor, many observers believe Merkel would likely have to fire him - which in turn could effectively end her current governing coalition and the conservative parties' decades-old alliance in national politics.
"The overwhelming majority of the German population supports this idea" - of turning the previously registered back at the borders - "and that's why we want to provide support today for implementing it", he said.More news: Bystander kills suspect at Washington Walmart
In a column for in the Frankfurter Allgemeine Zeitung, meanwhile, Seehofer wrote: "It is essential that the [European Union] summit takes a decision at the end of June".
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 situation is serious but still solvable".
In turn, Merkel praised Seehofer's "master-plan" by calling the document "a good foundation" for resolving the existing migration policy issues.
The row boiled over this week when a boat carrying Libyan migrants rescued at sea was refused permission to dock on either Italy or Malta. But pointedly, Kurz announced the plan with Seehofer, not Merkel, standing by his side.
The CSU is more conservative than Merkel's CDU and its paramount aim is to maintain its dominance in Bavaria.
Interior Minister Horst Seehofer of the CSU has been one of the fiercest critics of Chancello Angela Merkel's liberal stance that allowed a million asylum seekers into Germany since 2015.
"There is a context here of rising criminality, which to a statistical degree is part of the migrant problem", he said, adding that Democrats in the USA and Merkel in Germany both "neglected to their peril" the opposition among citizens to illegal immigration and lax border security.
Merkel quickly made clear that she disagreed.