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 global agreements.
Merkel has had an often-tense history with Seehofer, and their relationship became really hard after Merkel's 2015 decision to keep Germany's borders open as migrants streamed across the Balkans.
Merkel is reportedly aiming to negotiate individual deals with Germany's neighbors to allow Berlin to refuse refugees who have already been registered in another European Union country.
The political crisis in Germany erupted after Seehofer demanded that the German Chancellor agree to European rules on migration, and begin refusing migrants who arrive in other EU countries.
With neither leader budging, the conflict escalated over the weekend, leading to fears that the government would collapse.
Though Merkel had been lukewarm on Macron's idea of a European budget, in a declaration adopted by both leaders following the meeting they said they had agreed upon a proposal to establish one aimed at "competitiveness and convergence".
Macron also won a green light to push ahead with plans for a rapid-reaction military force, something Berlin had resisted for fear of undermining other European security initiatives. "Merkel's argument for Europe is substantial - but not popular".
Tech condemns Trump: Apple, Microsoft, Airbnb oppose separating families at the border
In the five weeks from the announcement, more than 2,300 children were taken from their parents and adult relatives. The audio of the 10 children is just a tiny percentage of what is happening at the U.S. border.
This is what Trump tweeted: "The people of Germany are turning against their leadership as migration is rocking the already tenuous Berlin coalition".
France and Germany may also strike a deal aimed at harmonising corporate taxes across the bloc, to stop multinationals from taking advantage of low-tax regimes in for example the Netherlands, Ireland or Luxembourg. "Big mistake made all over Europe in allowing millions of people in who have so strongly and violently changed their culture!" Merkel blocked the planned rollout last week, arguing that a bloc-wide solution is needed to what is a European problem. -Mexican border, a policy aimed at deterring illegal immigration. The CSU fears electoral disaster in upcoming regional elections. Still, polls suggest that its absolute majority in the Bavarian state legislature is in danger in the October 14 state election - and it is being challenged on the right by the far-right, anti-immigrant Alternative for Germany party.
In a sign of the frayed nerves, Germany's political and media world lurched into a brief panic Friday as several media outlets fell for a hoax tweet claiming Seehofer's CSU was quitting the coalition. "By now, the AfD has established itself as a protest party".
But they differ on its make-up, and Merkel faces the restraint that the German parliament must debate and vote on any military mission overseas.
Merkel said the two also agreed to enhance the effectiveness of the European Stability Mechanism, or ESM, which was established in 2012 to provide eurozone nations access to financial assistance in the event of crisis.
"How Germany acts will decide whether Europe stays together or not", Merkel told her CDU party's leadership at a meeting in Berlin, according to participants. "Of course, it would be good if there is a European solution, but in three years that hasn't been reached".