Meanwhile, Seehofer has also dropped his threat to quit.
The deal, which envisages setting up transit camps for migrants on the German-Austrian border, needs the approval of Merkel's other coalition partner and agreements with other European Union states to take back asylum seekers registered in their territories.
Angela Merkel returned from Brussels with an agreement forged, or critics would say fudged, with her European counterparts about the handling of refugees and migrants.
Merkel could have fired Seehofer.
The border deal, hailed by the German chancellor as a "good compromise", foresees setting up so-called transit centres on the southern border, where asylum seekers who have already been registered in other European Union countries will be held until they can be sent back to those countries. That would likely end the seven-decade partnership of the CDU and CSU, which have a joint parliamentary group, and would leave the government just short of a majority.
Her coalition partners have opted not to sink the government for now.
In a meeting with his party leaders on Sunday night, Seehofer offered to resign from his ministerial role and party leadership, reports said.
Top CSU officials had said they wanted to stay in government with Mrs Merkel's CDU.
The cantankerous Bavarian leader, who turns 69 this Wednesday, coyly said he would make a final decision on his job within three days.
The divisions within the German government over the issue are also being played out in other European Union countries, and three countries later said they were not part of the German deal: the Czech Republic, Hungary and Poland.
Her turnaround was prompted by her Interior Minister, Horst Seehofer, who has demanded that migrants at the border must have papers before advancing past the German welcome mat. "And as a result we will see a crash - damaging both parties." .
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.
Meanwhile for Merkel's troops, "the image of the country, our ability to act and our ability to govern" were at stake, said economy minister and close Merkel ally Peter Altmaier. Although she called the standoff "very serious", Ms. Merkel underlined her support for Germany's negotiation position with European Union partners, and again argued that this would be weakened if Berlin opts for a unilateral migration policy.
He said the two parties should be aware that the far-right Alternative for Germany, which has soared in prominence since a wave of migrants fleeing conflict and poverty headed to Germany in the summer of 2015, stood ready to benefit from a meltdown of the conservatives.