She has pledged instead to seek bilateral agreements with arrival and transit countries and a wider solution by the European Union, which holds its next summit on June 28-29, while admitting that this plan is "ambitious".
"Be smart America!" said the president, who is under mounting pressure to end the separation of immigrant families on the southern United States border.
In Germany, voters handed Merkel her poorest score in September's elections while giving seats for the first time to the far-right anti-Islam AfD.
In this Wednesday, June 13, 2018 photo, German Chancellor Angela Merkel, right, talks to Interior Minister Horst Seehofer, left, prior to the weekly cabinet meeting at the chancellery in Berlin.
Merkel said she will hold talks on bilateral agreements with other European countries at and around a June 28-29 EU summit.
"Crime in Germany is up 10% plus (officials do not want to report these crimes) since migrants were accepted", Trump tweeted, a day after he claimed German people were "turning against their leadership" over immigration. The decision sparked some opposition, most recently in the form of Interior Minister Horst Seehofer's open challenge to the policy, and a public poll showing 62 percent of Germans want to turn away asylum-seekers at the border.
By contrast, Merkel has warned of a resulting domino effect as Germany's neighbors rush to shutter their internal Schengen borders and is calling for a joint European solution to the "refugee crisis" to be reached within the next two weeks.
The CSU's top priority is a hard October state election in Bavaria in which it is trying to tamp down support for the anti-migration Alternative for Germany party.
The two leaders of Europe's biggest economies will seek to thrash out a compromise between Macron's bold vision for sweeping European Union change and Germany's stance that is more cautious, especially when it comes to finance.
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Merkel has said she is "favourable" to a French call to create a European Intervention Initiative of forces which could be deployed rapidly to deal with crises outside the framework of North Atlantic Treaty Organisation. She said her party will consider the results on July 1 "and decide how to proceed in light of what has been achieved".
Seehofer has earned the wrath of politicians across the political spectrum for appearing to seek a major confrontation with Merkel, threatening to place police at the border even if she rejected his plan, which would leave her little choice but to sack him.
"I have here in my hands figures from the Germany Ministry of the Interior under Minister Seehofer", reporter John Gizzi said.
Seehofer said his party was keen to find a way to limit the number of asylum seekers arriving in Germany.
"It is crucial that the European Union summit at the end of June reaches agreements that recognize Germany's burden in migrant policy", he said.
Seehofer and Merkel have long had an awkward relationship.
Rightwingers in her delicate governing coalition-as well as several northern European countries-remain hostile to France's push for a common eurozone budget, fearing taxpayers could foot the bill for fiscal irresponsibility in southern EU states.
In 2014, before more than a million migrants arrived in Germany, 6.08 million criminal acts were recorded - a higher rate than previous year.
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