Merkel is reportedly aiming to negotiate individual deals with Germany's neighbors to allow Berlin to refuse refugees who have already been registered in another European Union country. If she fails, the CSU vows to break its decades-old alliance with the chancellor's Christian Democrats, which would likely lead to new elections.
The number of applications for asylum in Germany dropped by 70 percent in 2017 compared to the previous year but Germany remains the main target for asylum seekers in the EU.
President Trump first made his claim that the crime rate in Germany is "way up" in Germany in a tweet on Monday and also asserted that migrants have "strongly and violently changed their culture" in Europe.
"We are working to make sure that the eurozone budget will be used to strengthen investment, also with the aim of strengthening convergence within the eurozone", Chancellor Merkel said ahead of the agreement.
Matteo Salvini, interior minister in the anti-establishment government that took office this month in Rome, has adopted a policy of blocking foreign humanitarian boats from Italian ports, which has triggered heated exchanges with France and the Netherlands.
The meeting came after months of back-channel discussions in which both sides tried to close the gap between their divergent visions for the European Union and the Eurozone, with both leaders making some concessions to the other.
While she has rejected unilateral action to turn back some migrants at the German border, Merkel has raised the possibility of forging agreements between two or more countries if an EU-wide asylum deal can't be reached.
"(Trump's) zero-tolerance policy is cruel.
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.
Mrs Merkel opposes the proposal that comes from a party facing a tough vote in its home base in Bavaria in October against a resurgent far-right Alternative for Germany (AfD), which has advocated harsh anti-immigration line.
"Our colleagues consider the latter option very unlikely and see a further muddling through with no clear victor but a substantially damaged Merkel as the most likely outcome".
German Interior Minister Horst Seehofer, left, talks to Chancellor Angela Merkel in parliament.
"The situation is serious but it can be overcome", he wrote, adding clinching an European Union deal at a June 28-29 summit was crucial. We see states that are turning inward, trying to find national solutions to problems that require European solutions. One Honduran asylum seeker killed himself in detention after U.S. authorities separated him from his wife and three-year-old son last month, The Washington Post reported.
"We do not believe that a European solution will be reached within two weeks - it has already failed to materialize for three years (since the height of the 2015 refugee crisis, note)", Soeder told dpa.