Trump said the two countries, through a "new strategic dialogue", would continue to boost joint security efforts in the Mediterranean and North Africa and would focus on "the urgent need to protect our nations from terrorism and uncontrolled migration".
Republicans, who hold majorities in both the House and Senate, have not been able to pass the immigration changes the president wants.
But leaders said funding for the wall could wait until after the November election.
The government has already been shut down once during Trump's presidency.
Congress has given the president some wall funding but far from the $25 billion he has requested. Democratic activists in the state are hoping to leverage high-profile clashes with the Trump administration over immigration, oil drilling in California's offshore waters, and the prospect of loosening federal pollution rules on cars, to help flip GOP congressional seats to the Democratic column. Numerous children have been accused by immigration officials of belonging to MS-13 and other violent gangs, an activity Trump has used to justify his "zero tolerance" policy of prosecuting immigrants caught entering the country without permission.
Trump's rhetoric and policy proposals surrounding immigration and the U.S. -Mexico border have been controversial ever since he announced his presidential campaign in June 2015.
Under withering public rejection and criticism from congressional Democrats and Republicans alike, Trump stopped taking children from their parents. The House is now in recess, returning after Labor Day.
Polar bear shot after attacking cruise ship guard
Such teams are a requirement for all cruise ships that visit the area. "We are extremely sorry that this incident has happened". In this case, one of the guards was attacked unexpectedly by a polar bear that had not been spotted.
In a thoroughly on-brand move, Trump went on a long Twitter rant that ended with him threatening to shut down the government if Democrats don't vote to build a Wall on the Mexico border. But they have the strength to derail legislation in the closely divided Senate.
The senators want the inspectors general for the departments of Homeland Security and Health and Human Services to investigate the abuse allegations immediately and to release any previous investigations into the charges.
Ultimately, it is the policy that led to the separation of some 2,500 children from their families - an issue Democrats exploited politically. Nita Lowey of NY and Lucille Roybal-Allard of California - called the $5 billion a waste that "only further enables this administration's obsession with cruel attacks on immigrants".
Trump also doubled-down Sunday on defending his administration's tough immigration enforcement policies amid the ongoing controversy surrounding the since-scrapped zero tolerance policy that separated illegal immigrant children from their parents at the border.
Updated 3:14 p.m. | One day after threatening a government shutdown over the issue, President Donald Trump signaled Monday he may not insist on full funding for his proposed southern border wall by the end of September.
A federal judge had ordered the reunions to be completed by Thursday but hundreds of children remain separated.
Committee Chairman Charles Grassley, R-Iowa, said Trump's crackdown on people illegally crossing the border from Mexico was well-intentioned but has had unintended consequences.