Merkel and Seehofer have been embroiled in a dispute for weeks over the interior minister's plan to start turning away migrants at the German border with Austria who have already registered elsewhere in the European Union (EU).
Rebel interior minister Horst Seehofer withdrew his threat to resign after the German chancellor agreed to tighten controls on the Austrian border by setting up transit centres to deal with migrants.
If the agreement reached is approved by the German government as a whole, "we will be obliged to take measures to avoid disadvantages for Austria and its people", Vienna's rightwing government warned.
Infighting began after Seehofer pledged to send back asylum seekers at Germany's border if they're already registered in another European Union country.
The sources said that in Sunday's private party meeting, Seehofer said he had a "conversation with no effect" with Merkel when they held talks on Saturday about the European Union migration deal, AFP news agency reported. Leaders of five countries considered possible locations of refugee camps outside the EU - Egypt, Albania, Morocco, Tunisia and Algeria - have said they are not interested in any such deal with the EU.
The centre-left Social Democrats, another partner in the coalition, must also accept the deal along with neighbouring Austria.
She told reporters afterward that "The security of our country begins on our borders".
Sebastian Kurz is Austria's current chancellor. "I have not studied it in detail but at first glance - and I have asked the legal services to look at it - it seems to me to be in line with the law", he told a news conference in Strasbourg.
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Seehofer's power over Merkel stems from an agreement under which the CSU replaces Merkel's CDU in Bavaria, Germany's largest and wealthiest state and home to BMW, Siemens and Adidas and football champions Bayern Munich.
To politically survive, Merkel could attempt a minority government, seek a new coalition partner in the ecologist Greens or pro-business Free Democrats, or orchestrate a no-confidence vote in parliament that could trigger new elections.
"It is worthwhile to prevent this conflict from becoming a real war", she said, adding however that this "would require both sides" to take steps. Seehofer is a member of the Christian Social Union, an ally of Merkel's party.
"So they agreed in principle to a concept that was denied by the SPD and the former grand coalition in 2015 already, and Merkel at that time actually backed this agreement".
It was reported that Merkel had believed that the European solution could satisfy CSU's ultimatum, which was due on Sunday, otherwise Seehofer would bypass Merkel to implement a tougher asylum policy.
It is the impending Bavarian state election in October that forced Mr. Seehofer's hand in seeking a confrontation on the migration issue.
As he entered a CDU crisis meeting yesterday, deputy leader Armin Laschet said the sister parties "want to hold onto" their alliance. He accused the CSU of a ruthless attitude towards refugees, insisting that the "C" in CDU and CSU no longer stood for "Christian" but for "chaos".