Trump's comments came after German Chancellor Angela Merkel agreed to find a solution to the migrant issue by the end of the month, with interior minister Horst Seehofer backing down from his threat to bypass her on border controls - for now.
Merkel has reportedly urged Seehofer to give her until the European Union summit at the end of June, but the Bavarian has kept up pressure for a solution to be found in the coming days.
Merkel has had an often-tense history with Seehofer, and their relationship became really hard after Merkel's 2015 decision to keep Germany's borders open as migrants streamed across the Balkans.
Seehofer has vowed to refuse entry to undocumented migrants and those who have already registered in another European Union member country, part of what the Bavarian conservatives are calling an "asylum reversal".
The chancellor, who is scheduled to meet her French counterpart Emmanuel Macron next week, said Germany and France would seek to set the agenda for European Union cooperation on defense, security and foreign policy ahead of the June summit. "If we're in a talks situation in a few weeks, we'll talk", she said.
Merkel opposes this, saying that such unilateral measures represent a setback to the EU's Schengen open-border system and any chances of overcoming deep divisions in the bloc.
Seehofer has been one of the fiercest critics of Merkel's liberal stance, under which over one million asylum seekers have been admitted into the country since 2015.
Belgium finally break Panama down as De Bruyne, Hazard, Lukaku deliver
He also has a history now of popping up in World Cup openers: Four years ago, he scored the victor in a 2-1 triumph over Algeria. Panama was unable to duplicate what Senegal accomplished in 2002 as the last team to win in its World Cup debut.
In an unprecedented challenge to her 13 years as Germany's chancellor, a resolution by her interior minister, Horst Seehofer, is set to be passed on Monday, party aides told German newspaper Bild Zeitung.
Popular misgivings over the migrant influx have given populist and anti-immigration forces a boost across several European nations, including Italy and Austria where far-right parties are now sharing power. That figure fell a year ago to less than 200,000.
But she reiterated her opposition to Germany unilaterally closing its borders as this would pass the migrant burden on to neighbouring countries, "unleashing undesired domino effects".
Merkel is due to hold a press conference on Monday.
Seehofer and Merkel have long had an awkward relationship. Merkel blocked the planned rollout last week, arguing that a bloc-wide solution is needed to what is a European problem.
A senior German government official said that Finance Minister Olaf Scholz and his French counterpart resumed negotiations on euro zone reforms on Tuesday morning after narrowing differences in talks over the weekend.
On common defence, Merkel has said she is "favourable" to Macron's demand for a rapid reaction force dubbed the European Intervention Initiative.