Homeland Security Secretary Kirstjen Nielsen warned Sunday that the illegal immigrant caravan heading toward the U.S. could be exploited by cartels that control most of the illegal flow of people through Latin America.

Ms. Nielsen also praised the efforts of Mexico and Central American governments she said are working with the U.S. to try to contain the caravan, rather than enable it.

While some among the once-5,000 member caravan have given up and returned to Honduras, local reports say about 2,000 people have barged into Mexico and vow to press on to the U.S., defying the will of the Mexican and American governments.

SEE ALSO: Migrant caravan re-forms in Mexico: ‘We are going to reach the United States’

Warnings of a get-tough policy from U.S. officials have done little to deter the migrants, who for years have seen relatives and neighbors easily jump the border to enter the U.S. with little consequence. The ease of entering is a selling point for the cartels, who control the drug and human smuggling routes into the U.S. and require payment of a “mafia fee” just to cross the U.S.-Mexico boundary line.

Court records show that fee typically runs from $1,000 to $2,000. That doesn’t include thousands of dollars in other fees that cover foot guides, drivers, stash houses and the rest of the illegal journey.

“While we closely monitor the caravan crisis, we must remain mindful of the transnational criminal organizations and other criminals that prey on the vulnerabilities of those undertaking the irregular migration journey,” Mr. Nielsen said in a statement Sunday.

SEE ALSO: 500 caravan members voluntarily return to Honduras: ‘There were unruly people, I was disappointed’

She also repeated U.S. backing for the governments who have tried, under threats from President Trump, to stem the flow.

“We fully support the efforts of Guatemala, Honduras and Mexico, as they seek to address this critical situation and ensure a safer and more secure region,” the secretary said.

Mr. Trump has said he would pull U.S. foreign assistance from Central American countries and would “seal” the border, including nixing the free trade agreement he’s finalizing with Mexico, unless those nations find ways to halt the caravan.

He has also said he will deploy the U.S. military — a step beyond the National Guard troops he previously asked be sent to the border.

Mexican authorities had attempted to keep the caravan in Guatemala, processing people individually to enter either to claim asylum or to get a visitor visa. But thousands of migrants decided not to wait and burst through fencing or paid to be ferried across the river into Mexico, circumventing the border guards.

The caravan began a week ago in Honduras. The Associated Press reported that Guatemalan officials calculate some 5,400 people had entered their country from Honduras since the caravan began. Perhaps 2,000 have returned home.