Mexico president chides Trump: Mexican America 'sounds nice'

Mexico President Claudia Sheinbaum on Wednesday suggested North America including the United States could be renamed "Mexican America" - an historic name used on an early map of the region - in response to US President-elect Donald Trump's pledge to rename the Gulf of Mexico the "Gulf of America."

"Mexican America, that sounds nice," Sheinbaum joked, pointing at the map from 1607 showing an early portrayal of North America.

The president, who has jousted with Trump in recent weeks, used her daily press conference to give a history lesson, flanked by old maps and former culture minister Jose Alfonso Suarez del Real.

"The fact is that Mexican America is recognized since the 17th century... as the name for the whole northern part of the (American) continent," Suarez del Real said, demonstrating the area on the map.

On the Gulf of Mexico, Suarez del Real said the name was internationally recognized and used as a maritime navigational reference going back hundreds of years.

Trump floated the renaming of the body of water which stretches from Florida to Mexico's Cancun in a Tuesday press conference in which he presented a broad expansionist agenda including the possibility of taking control of the Panama Canal and Greenland.

Sheinbaum also said it was not true that Mexico was "run by the cartels" as Trump said. "In Mexico, the people are in charge," she said, adding "we are addressing the security problem."

Despite the back and forth, Sheinbaum reiterated that she expected the two countries to have a positive relationship.

"I think there will be a good relationship," she said. "President Trump has his way of communicating."