The Department of Homeland Security has no intention of paying $50,000 to each of the 6,000 migrants who traveled in caravans from Central America to Tijuana, a spokeswoman said Wednesday afternoon.

"Secretary [Kirstjen] Nielsen has made clear that being a member of a caravan does not give them special rights for entry into this country and now it looks like some of these migrants understand that the Trump administration’s commitment to enforcing the rule of law, and their own likely lack of a legitimate claim of asylum, means they should return home," DHS spokeswoman Katie Waldman said in a statement.

A group of the Guatemalan and Honduran migrants who have been temporarily living in Tijuana since arriving there in mid-November marched about two hours to the U.S. Consulate on Tuesday with a tall order for the Trump administration.

[Opinion: Asylum seekers demanding $50,000 a pop are not asylum seekers]

Some members carried signs that stated: “You got it wrong, Trump. We asked for jobs and you responded with weapons. That is not polite. If asking for work is troublesome, then I am totally confused. La Caravana.”

They submitted a petition for the U.S. government that stated everyone in the caravan should be admitted into the country or be paid $50,000 each to return to their home countries.

The petitioners gave the U.S. 72 hours to respond.

"[T]he overwhelming majority of caravan members are not legitimate asylum seekers — if they were they would seek refuge in the first safe country they entered," said Waldman. "Yet, predictably they turned down Mexico’s generous offer in search of economic opportunity or family reunification in the United States."

Those who illegally enter the U.S. from Mexico still have the opportunity to apply for asylum if they claim a credible fear of returning home. That claim triggers the pre-asylum process.

Last fiscal year, only 9 percent of those who claimed a credible fear and had their case heard by an immigration judge were granted asylum.