ROUGH CUT (NO REPORTER NARRATION) A U.S.-bound caravan of thousands of mostly Honduran migrants who have been condemned as unwelcome by President Donald Trump, began moving into Mexico on Sunday (October 21), shadowed by hundreds of Mexican police en route to the border city of Tapachula.

The migrants have defied threats by Trump that he will close the U.S.-Mexico border if the caravan advances and warnings from the Mexican government that they risk deportation if they cannot justify seeking asylum in Mexico.

Trump tweeted on Sunday "Full efforts are being made to stop the onslaught of illegal aliens from crossing our Southern Border.

People have to apply for asylum in Mexico first, and if they fail to do that, the U.S. will turn them away.

The courts are asking the U.S. to do things that are not doable!" Dressed in riot gear, police arrived along a southern highway in several buses, ahead of the throngs of men, women and children marching north after they crossed the Guatemalan border.

An unidentified police officer told Reuters there were no orders to block the caravan.

As a military helicopter circled overhead, migrants who said they were fleeing a toxic mix of violence, poverty and corruption in Central America wondered if police would seek to turn the caravan back.

Most said they felt safer advancing as part of a large group.

Trump has threatened to halt aid to Honduras and Guatemala, and potentially close the U.S. border with Mexico with the help of the military if the migrants' march is not stopped.