Mexican President Claudia Sheinbaum has suggested that North America, including the United States, could be called "Mexican America" as shown in an old map.

Sheinbaum made the comment half-jokingly during a news conference on Wednesday. It was an apparent response to US President-elect Donald Trump's remark on the previous day that the Gulf of Mexico should be renamed the Gulf of America.

The Mexican president floated her idea by showing reporters a map from the 17th century. It described North America as "America Mexicana" in Spanish, which means Mexican America.

Sheinbaum said with a smile that the name "sounds nice, doesn't it?"

She also used the same map to explain that the Gulf of Mexico was already an internationally recognized name at that time.

In response to a reporter's question, Sheinbaum brushed aside another remark by the US president-elect that Mexico is run by drug cartels. She said it is "false."

But she added that she thinks there will be a good relationship with Trump. She said she doesn't see why there would be a bad relationship.

Immigration and drug control are some of the key challenges facing the two countries.

Trump has said he would impose 25-percent tariffs on imports from Mexico and Canada if those countries do not stop the flow of illegal immigrants and drugs into the US across their borders.