US President Donald Trump is moving to target Latin American drug cartels with the military, US media said, after Washington designated several narcotics trafficking groups as "terrorist" organisations this year.

The New York Times reported on Friday that Trump has directed the Pentagon to use military force against cartels deemed terrorist organisations.

The Wall Street Journal said the president ordered options to be prepared, with the use of special forces and the provision of intelligence support under discussion, and that any action would be coordinated with foreign partners.

White House spokeswoman Anna Kelly, while not confirming the reports, said 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 organisations."

The United States designated Venezuela's Tren de Aragua, Mexico's Sinaloa Cartel and six other drug trafficking groups with Latin American roots as terror groups in February.

The US embassy in Mexico released a statement later on Friday, saying both countries would use "every tool at our disposal to protect our peoples" from drug trafficking groups.

But the Mexican foreign ministry stressed that Mexico "would not accept the participation of US military forces on our territory."

Trump's administration has since added another Venezuelan gang, the Cartel of the Suns, which has allegedly shipped hundreds of tons of narcotics into the United States over two decades.

The United States accuses Venezuela's President Nicolas Maduro of leading that cartel – an allegation Caracas has rejected as a "ridiculous smokescreen".

Trump signed an executive order on January 20, his first day back in the White House, creating a process for the designation of the cartels, which he said "constitute a national-security threat beyond that posed by traditional organised crime."

His Mexican counterpart Claudia Sheinbaum insisted on Friday that there would be "no invasion" of her country.

Sheinbaum has made strenuous efforts to show Trump she is acting against Mexico's cartels, whom he accuses of flooding the United States with drugs, particularly fentanyl.

"We are cooperating, we are collaborating, but there will be no invasion. That is absolutely ruled out," she said.

On a related front, the Wall Street Journal reported on Friday that Trump is considering reclassifying marijuana as a less dangerous drug. (AFP/Reuters)