Originally posted by the Voice of America. Voice of America content is produced by the Voice of America, a United States federal government-sponsored entity, and is in the public domain. Mexico to let Migrants Remain While US Asylum Claims Proceed by Associated Press MEXICO CITY -- Mexico has agreed to a U.S. proposal to let third-country migrants remain in or be returned to Mexico while their claims for asylum in the United States are being processed. The decision was a historic one for Mexico, which has traditionally refused to accept the return of any migrants who aren't Mexican. Mexico's Foreign relations Department said Thursday the move i a temporary, humanitarian measure. The administration of U.S. President Donald Trump has been struggling with an increase in asylum claims and limits on its ability to detain asylum seekers