Merkel has supported free movement across Europe but has been facing pressure to limit that movement.
Among the proposals is a plan to send back to Austria asylum seekers arriving in Germany who can not be returned to their countries of entry into the European Union.
"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", Mr Seehofer told reporters as he was leaving the CDU's Berlin headquarters.
Under the German deal, migrants who have already applied for asylum in other European Union countries will be held in transit centres on the German border with Austria while Berlin negotiates bilateral accords for their return.
All new migrants would have to be screened at the centers and determined if they are eligible to seek asylum in Germany.
Relations between the United States and other industrialised powers have turned increasingly tense as Trump has pushed his "America First" stance with punishing consequences for trading partners, irregardless of whether they are allies or adversaries.
Kurz called for an anti-migration "axis of the willing" with Germany and Italy to push in a bid for heightened restrictive border policies within the European Union nations.More news: Pickford is penalty hero as England reach quarter finals
More news: USA wants to reduce Iran's oil revenue to zero
More news: Trump urges Saudis to raise oil output ‘by two million barrels’
Meanwhile Hungary's anti-migrant Prime Minister Viktor Orban, said Budapest was open for talks with Germany if Berlin managed to strike a migration deal with neighbouring Austria, whose Chancellor Sebastian Kurz is, like Orban, an immigration hardliner. "We want a humanitarian, but also realistic, migration policy", she told a news conference.
The euro rose after Merkel and interior minister Horst Seehofer, her antagonist who had threatened to resign, ended their two-week standoff late on Monday. "With this the very spirit of partnership in the European Union is protected and at the same time, it is a decisive step towards organizing and managing secondary migration", Merkel said.
Seehofer had been in a showdown with the German Chancellor, offering his resignation on Sunday in protest over Merkel's reluctance to accept his plans to reverse the country's generous policies towards migrants.
In agreeing to form Merkel's coalition government earlier this year, the SPD expressly said it opposed migrant transit centers at the border, meaning it could possibly veto the deal.
"We don't need masterplans, we need good craftsmanship", Andrea Nahles, head of the SPD said.
Weeks of "Merkel-bashing", however, have failed to help the CSU, as a Forsa poll last week showed around 68 percent of Bavarians backed Merkel's quest for a Europe-wide answer to migration rather than Germany going it alone.
The party reluctantly agreed to renew its alliance with the CDU and CSU after suffering its worst post-war result in last September's election.
Both sides hammered out "a truly good compromise ... after a tough struggle and hard days", Merkel said, describing the holding and processing centres.