MEXICO CITY - Mexican President Claudia Sheinbaum on Monday warned search engine Google in a second letter that her government will take legal action unless the company reinstates the name of the Gulf of Mexico on its maps.

Google does not have the right to rename the entire Gulf of Mexico to the Gulf of America to comply with an executive order from US President Donald Trump, the Mexican leader told a morning press conference at the National Palace here.

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Once again, Sheinbaum explained that Trump's executive order applies only to the continental shelf of the United States, so the search engine, which offers mapping services worldwide, does not have the authority to change the name of the entire gulf, to which Mexico and Cuba also have territorial claims.

"We are going to wait for Google's response and if it does not, we will proceed in court," Sheinbaum said.

The president read aloud Google's first response to the Mexican government, in which it argued that as a private company outside international treaties, it has chosen to use Gulf of America for users in the United States, Gulf of Mexico for users in Mexico, and Gulf of America and Gulf of Mexico for the rest of the world.

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"We do not agree," said Sheinbaum. "But under no circumstances does Mexico accept the renaming of any geographic area that includes part of its national territory and that is under its jurisdiction."

The second letter, which she also read aloud, includes the historical and legal data that underpin Mexico's request.