The president has made the claim as he defends his administration's new "zero tolerance" policy that calls for the criminal prosecution of all adults apprehended attempting to cross the US border illegally.
German Chancellor Angela Merkel, who Trump met with last week at the G7 summit, has faced political headwinds in the country since she implemented an open-door policy in 2015 in an effort to lead the way in response to the refugee crisis.
Merkel was due to meet with Italy's newly-minted Prime Minister Giuseppe Conte on Monday, and the following day with French President Emmanuel Macron.
"We want Europe to find its place in a multilateral world, we want Europe to play its role when it comes to defending values and convictions, promoting prosperity, more peace in the world and preserving environment", she said.
But she reiterated her opposition to Germany unilaterally closing its borders as this would pass the migrant burden on to neighboring countries, "unleashing undesired domino effects".
While Merkel is determined to reach a European solution, Falter argues that she could eventually compromise to save her government.
Horst Seehofer, leader of Christian Social Union, Bavarian party Allied and Minister of German interior, imposed on Monday an ultimatum of two weeks, in which Chancellor must agree with European partners formulas that allow him to reduce arrival of Asylum seekers in Germany and to prevent asylum seekers in anor EU country from crossing German borders. A struggle over migration policy has threatened her government.
A recent Forsa survey showed that Merkel is still popular among Germans, with about a 50 percent approval ratings. She has meetings planned this week with the leaders of Italy and France, and an European Union summit is scheduled June 28-29. The CSU's share of the vote in Bavaria dropped 10.5 percentage points to 38.8 percent, with Alternative for Germany a major beneficiary.
On Monday, the European Union asylum office said the number of people applying for global protection in Europe has plunged but remains higher than before 2015.
Seehofer and Merkel have long had an awkward relationship.
Merkel told reporters she was still convinced that Europe needed to work together to combat the causes of the refugee flow by helping improve conditions in the countries of origin while at the same time increasing security at Europe's outer borders and cracking down on smugglers.
Italy and France have also become involved in the migrant debate, with Italy's interior minister Matteo Salvini, who is the deputy Prime Minister of the country, refusing to accept new refugee boats and calling for asylum seekers to be equally distributed across the European Union, rather than being hosted by the first country they land in.
She said she would report back July 1 on the results of her negotiations, and that as far as she's concerned it's not yet clear what will happen if there's no European deal on the divisive topic.
Merkel said the primary objective of the budget, which could go into effect in 2021, would be to fund "investments and convergence measures". The CSU lost thousands of voters to the far-right Alternative for Germany (AfD) party in federal elections past year, and is fearful of further losses.
Once again the two sister parties, Merkel's CDU and the Bavarian CSU, have been fighting over immigration.
Merkel and Macron said they hoped to have a more detailed plan by the end of the year.