U.S. lawmakers on Sunday expressed doubts that they could advance legislation to toughen the asylum process for migrants in the next two weeks, as sought by President Trump and Vice President Mike Pence after the administration delayed a planned weekend round of deportations.

Democrats signaled they would rather focus on a comprehensive immigration overhaul or measures to fund the asylum process at the border. Republicans, meanwhile, favored legislation to limit asylum options and build Mr. Trump’s proposed border wall.

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