At issue Monday was whether the CSU would give her time to try to reach such a deal.
Mr Seehofer will give Mrs Merkel two weeks to gain support from her European Union partners to halt the policy, or he will carry out the order himself.
Speaking at a Monday briefing, the key Merkel ally and Christian Social Union (CSU) party head said that the chancellor effectively approved nearly all provisions of his so-called "master plan".
A CSU leadership meeting Monday in Munich is likely to authorise Seehofer to go ahead with his plan - but it's unclear at what point leaders want it to take effect.
Seehofer's "migration master plan", which Merkel last week refused to endorse, would see asylum seekers arriving at Germany's borders turned away if they have no identification papers, have already had an asylum claim rejected in Germany, or are already registered in another country in the EU - proposals that rights group say contravene European and worldwide agreements.
There is even talk that the 70-year-old conservative alliance between the CSU and Merkel's Christian Democrats (CDU) could fall apart.
European Union countries are once again at loggerheads over migration, triggered by Italy's recent refusal to allow a rescue ship carrying 630 migrants to dock. That banished - if only for now - the spectre of Seehofer pushing through his proposal in defiance of the chancellor, which would risk bringing down her government.
"It is not in the CSU's interest to topple the chancellor, to dissolve the CDU-CSU union or to break up the coalition", Seehofer told Bild in remarks published Sunday.
Seehofer told reporters he would prepare the measures but wait until after the European Council summit at the end of next week to implement them, in order to see whether Merkel could reach an agreement with EU leaders. Seehofer has said these migrants should be turned away at the German border whereas Merkel has said this can only happen with the agreement of the relevant European Union states.
Though the intensity of their current dispute is unprecedented, Merkel and Seehofer have been squabbling over refugee issues since 2015.
The CSU is more conservative than Merkel's CDU and its paramount aim is to maintain its dominance in Bavaria.
Seehofer last week defied Merkel to announce a tough new immigration policy that would see some asylum seekers turned away at the borders of Germany. However, Merkel has been unyielding in defending her initial decision to keep Germany's borders open, telling lawmakers earlier this month that "in an exceptional humanitarian situation, Germany behaved very responsibly".
She promised to pursue bilateral agreements on the distribution of asylum seekers as she meets with European leaders ahead of the EU summit at the end of the month. Merkel said she would first present the results of the talks to her own party on July 1 and then discuss them with her Bavarian allies.
But after the pair agreed last October to try to limit Germany's refugee intake to 200,000 a year - a policy Seehofer had long called for and Merkel had previously ruled out - tensions seemed to fade.