President Trump has ordered the American military to draw up plans to go after drug cartels in Mexico and elsewhere, according to reports, but the military may have more than just the heavily armed druglords to deal with if it does.

Any cooperation with American troops on Mexican soil is “absolutely off the table,” President Claudia Sheinbaum of Mexico told reporters on Friday.

Ms. Sheinbaum was responding to a New York Times report that Mr. Trump secretly signed a directive ordering the Pentagon to prepare options for the use of military forces against drug cartels in Latin America.

ABC News also reported on the directive but said there is no imminent use of military assets planned.

A legal framework for such action already exists, according to the secretary of state, Marco Rubio, whose department designated six cartels as terrorist organizations in February.

“We cannot continue to just treat these guys as local street gangs,” Mr. Rubio said during a Wednesday interview with a Catholic broadcaster, EWTNS. “They have weaponry that looks like what terrorists, in some cases armies, have.”

Mr. Rubio said the terrorist designation allows intelligence agencies and the Department of Defense to target the cartels and their operations.

“So what it changes is it gives us legal authorities to target them in ways you can’t do if they’re just a bunch of criminals. It’s no longer a law enforcement issue.  It becomes a national security issue.”

But the idea of American military operations in her country does not sit well with Ms. Sheinbaum, who is already engaged in delicate trade negotiations with the American president.

“We cooperate, we collaborate, but there will be no invasion,” she told reporters. “It’s off the table, absolutely off the table.”

One security analyst says a military offensive against the cartels could devastate relations between the two countries without accomplishing its goals.

“It’s not a welcome development,” a leader at the Global Initiative against Transnational Organized Crime, Cecilia Farfán-Méndez, said.

“And beyond the narrative, it seems to me that once again there’s been a misdiagnosis of these illicit markets and how we can weaken and dismantle them,” she told the Guardian.

The Pentagon declined to comment to The New York Sun about the directive and referred inquiries to the Trump administration.

The White House did not comment on the reported directive but reiterated that some cartels are now classified as terrorist groups.

“President Trump’s top priority is protecting the homeland, which is why he took the bold step to designate several cartels and gangs as foreign terrorist organizations,” the White House deputy press secretary, Anna Kelly, said in a statement to the Sun.

Mr. Trump began the process of designating some cartels as terrorist organizations on his first day back in the White House in January. 

An executive order signed on January 20 said it is the policy of the United States “to ensure the total elimination of these organizations’ presence in the United States and their ability to threaten the territory, safety, and security of the United States.”

Mr. Trump has also deployed thousands of troops to the areas near the Mexican border to not only combat illegal immigration but also to stop the flow of fentanyl and other drugs into the United States.