Seehofer wants to turn some migrants away from German borders, but said a unilateral move to turn them back could divide the chancellor's coalition.
Merkel is seeking a consensus on the issue from neighboring countries.
"It's in Germany's interest to achieve a controlled migration in good partnership with our European neighbors," she said.
Seehofer threatened Monday to turn back migrants if the German leader doesn't secure a deal within two weeks.
The deadline came after Merkel reached out to coalition partners to take back migrants who would be refused entry in Germany under its tough immigration policy.
The conflict stems from a challenge by Bavaria's Christian Social Union, the sister party to Merkel's Christian Democratic Union, to her "open door" policy for refugees from war-torn nations like Syria and Libya. Seehofer is chairman of the CSU.
Merkel accepted the deadline and said she will attempt to solidify a deal by the EU summit later this month, and report to her party by July 1.
"Whoever knows Europe, realizes this is no easy task," Merkel told reporters Monday, adding "we have a particular responsibility" to refugees.
As Merkel conceded to the deal Monday, President Donald Trump criticized the German asylum policy.
"The people of Germany are turning against their leadership as migration is rocking the already tenuous Berlin coalition," Trump tweeted. "Crime in Germany is way up. Big mistake made all over Europe in allowing millions of people in who have so strongly and violently changed their culture!"