Mexico City, Mexico - Mexican President Claudia Sheinbaum said on Monday she wants to avoid conflict with the US following the death of two US agents operating on Mexican soil without permission from the federal government.

Both governments traded diplomatic jabs following the incident last week involving what US media outlets have said were CIA agents.

Mexico accused the agents of potentially violating national security laws, while Washington attacked Sheinbaum as showing a lack of sympathy for the fallen Americans.

"We don't have any desire to get into a conflict with the United States," Sheinbaum said during her regular morning press conference.

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The two US agents died in a car accident on April 19 while returning from an operation to dismantle six drug laboratories in the mountainous northern state of Chihuahua.

Sheinbaum has said the Mexican federal government did not know the officers were operating in this country.

On-the-ground operations of US security officials in Mexico are highly controversial.

The Trump administration has pushed for drone strikes and US ground troops to attack Mexican drug cartels. But Sheinbaum has repeatedly rejected this offer, calling instead for using US intelligence to target cartel leaders.

She has stressed that US-Mexico security cooperation should be done through a "framework of respect" for local laws, arguing the case of the two fallen agents should be seen as an "exception."

Mexican criticism of the operation led to backlash from White House press secretary Karoline Leavitt, who said that "some sympathy from Claudia Sheinbaum would be well worth it for the two American lives that were lost."

On Saturday, Mexican officials reiterated that immigration records showed the US agents entered the country as "visitors, without permission to carry out paid activities."

They were collaborating with state authorities in Chihuahua, a border state governed by the conservative National Action Party (PAN). It is largest opposition party against Sheinbaum's left-leaning Morena.

The state prosecutor's office initially said the agents had participated in a local police operation to destroy clandestine drug laboratories.

The agents later said they were in the area for a workshop on drone usage, and requested a police convoy to escort them out of the area.