Mexico City, Mexico - Mexico will take Google to court if it insists on changing the Gulf of Mexico's name to "Gulf of America" for Maps users in the US, President Claudia Sheinbaum said Monday.

Sheinbaum said her government had written again to the US company arguing that President Donald Trump's executive order on the subject only applies to the part of the continental shelf belonging to the US.

"Google has no right to rename Mexico's continental shelf, nor does it have any right to rename Cuba's continental shelf, because the Gulf of Mexico is divided among the three countries," Sheinbaum said at her daily news conference.

The letter informs Google that "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," she said.

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"We will wait for Google's response and, if not, we will proceed in court," Sheinbaum added.

Sheinbaum had announced on Friday that her government was considering legal action against Google, saying: "If necessary, we will file a civil suit."

Trump signed an executive order renaming the Gulf of Mexico soon after his January 20 inauguration.

In response, Sheinbaum cheekily suggested calling the US "Mexican America," pointing to a map dating back to before 1848, when one-third of her country was seized by the US.

Google, which is part of tech giant Alphabet, said that users of its Maps app in Mexico would continue to see the name "Gulf of Mexico" while those in third countries would see both names.

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Sheinbaum presented a letter she said Google had sent to her Foreign Minister Juan Ramon de la Fuente explaining its position and offering to pursue a "constructive dialogue" about the issue, including through a potential face-to-face meeting.

The company said the name change was "consistent with our normal operating procedure to reflect on our platforms geographic names prescribed by different authoritative, government sources, including reflecting where authoritative sources may differ."

Apple has also renamed the body of water the "Gulf of America" for US users of its mapping application to comply with Trump's order.