But separate reports from sources within the CDU's Bavarian sister party, the CSU, indicated Mr Seehofer had offered to resign both as leader of the CSU and as interior minister.
She also pledged to conclude bilateral agreements with European partners such as Greece and Spain, with the goal of returning asylum seekers, who first entered the EU soil from these countries, but later arrived in Germany.
Merkel maintains that a plan to regulate immigration that European Union leaders approved Friday and bilateral agreements in principle that she hashed out with some countries for them to take back migrants would accomplish what Seehofer seeks.
After Merkel rejected the plan, Seehofer set the chancellor a deadline of July 1 to find a "European solution" to the issue of so-called "secondary migration", referring to asylum-seekers crossing internal EU borders after having already applied for asylum elsewhere in the EU.
He and his Bavarian Christian Social Union (CSU) party - a deeply conservative outfit allied for decades with Merkel's centre-right Christian Democratic Union of Germany (CDU) - argue the move would simply implement EU law known as the Dublin regulation.
"The sum total of everything we have agreed upon has the same effect" as what Seehofer has demanded, Merkel said in an interview with ZDF television, as reported by AP. The CDU's leaders, who are now gathered in Berlin for a second straight day of discussions, said they still see room for a compromise solution in the migration dispute.
Nevertheless, the anti-refugee, anti-Islam Alternative for Germany (AfD) was propelled into federal parliament for the first time previous year by outrage over immigration, leading to months of paralysis while Merkel struggled to find a workable coalition.
But he also struck a conciliatory tone, saying "there is an abundance of possibilities. for compromises", without specifying what they were.
If Seehofer resigns, he added, that wouldn't automatically mean the CSU's other ministers being withdrawn from the government.
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Despite tendering his resignation, the interior minister said he wanted to meet with Merkel on Monday before making a final decision.
Senior CSU lawmaker and former interior minister Hans-Peter Friedrich wrote on his Twitter account that the CDU and CSU wouldn't let themselves be divided.
Facing a state election in October, the Bavaria-only CSU hopes to win back votes eroded by the anti-migration Alternative fuer Deutschland and prevent the bordering state from being further impacted by migration.
The document circulated by Merkel to her coalition partners after the summit said 14 countries had agreed "on a political level" to take back some migrants who had passed through other European Union countries on their way to Germany.
"CDU and CSU have no interest in a split and the chances are over 90% for the coalition to survive for now", said retired politics professor Eckhard Jesse.
However, the more conservative CSU believes its credibility is at stake as it tries to curb support for the anti-migration Alternative for Germany party in the upcoming Bavarian election.
"It was a mistake that will follow us for a long time", he said at the time.
He said: "After intensive discussions between the CDU and CSU we have reached an agreement on how we can in future prevent illegal immigration on the border between Germany and Austria".