Her Christian Democratic Union (CDU) and its sister party CSU have suffered heavy losses in the country's federal elections past year, while the far-right Alternative for Germany (AfD) scored record gains and entered the parliament for the first time.
He said he would go ahead with preparations to block some asylum-seekers at the border in case Merkel's negotiations on getting other countries to take back migrants don't bear fruit.
At issue Monday was whether the CSU would give her time to try to reach such a deal.
Citing unidentified participants, dpa reported that Seehofer told a leadership meeting of his Christian Social Union party on Monday in Munich that he wants to start by turning back people against whom authorities have issued a formal entry ban.
HORST SEEHOFER: This is scandalous.
"No one in the CSU has an interest in bringing down the chancellor, dissolving the CDU-CSU joint parliamentary group, or blowing up the coalition", Seehofer was quoted as telling the Bild am Sonntag newspaper.
"The situation is serious but still solvable", he wrote.
While Merkel would welcome a reprieve from an immediate crisis in her coalition, she is still under intense pressure to deliver a deal with European Union partners who are deeply divided. "The pair looks vulnerable to test 1.1500, but could fall much further if the crisis in Germany spins out of control", he added.
Most first arrived in Bavaria, which borders Austria.
The calls for tougher policies have come even though the number of people reaching European shores in search of protection has declined.
The current European Stability Mechanism (ESM), introduced in 2012 to deal with the eurozone crisis, will be turned into a European monetary fund, which can offer loans to struggling EU countries, and better insulate the single currency from future crises.
In a tweet he said that migrants in Europe were responsible for a rise in crime in Germany and for violently changing the culture.
But the veteran politicians have often clashed.
Saying he appreciated Merkel's acknowledgment of Italy's situation, Conte reiterated his view that European Union accords that link asylum-seekers to the first country they reach should be replaced.
The row threatens to scupper Merkel's three-month-old coalition and limits her capacity for agreeing to far-reaching euro zone reforms, of which many in her conservative bloc are skeptical.
Merkel quickly made clear that she disagreed. Merkel has asked the CSU to be patient, a request that the Bavarians have ignored.
Seehofer also sacked Jutta Cordt, the head of the Office for Migrants and Refugees (BAMF), an interior ministry spokesman said late Friday.