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 United States “Mexican America”, pointing to a map dating back to before 1848, when one-third of her country was seized by the United States.
Google, which is part of tech giant Alphabet, said 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.
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.
It 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.
© Agence France-Presse