Mexico City, Mexico — Mexico's president took a swipe at Donald Trump on Wednesday, saying that the United States should be called "Mexican America," after Trump's vow to rename the Gulf of Mexico the "Gulf of America."

At her regular morning press conference, Claudia Sheinbaum displayed a 17th-century world map showing North America as "Mexican America."

Pointing out that the Gulf of Mexico was the name recognized by the United Nations, she turned the tables on Trump, saying: "Why don't we call it (the United States) Mexican America?"

"It sounds nice, doesn't it?"

"He talked about name, we too are talking about the name," she said, while assuring that she expected to have "good relations" with the incoming US president.

Trump, who will be sworn in for a second term on 20 January, said Tuesday he planned to rename the Gulf of Mexico "the Gulf of America, which has a beautiful ring."

"It's appropriate. And Mexico has to stop allowing millions of people to pour into our country," he said.

He also claimed that Mexico was run by drug cartels, to which Sheinbaum responded that "in Mexico, the people rule."

In the run-up to his return to office, Trump has repeatedly lashed out at Mexico, threatening to impose stiff tariffs on imports from one of the United States' biggest trading partners unless it halted the flow of illegal migrants and drugs across the border.

He has also revived a threat from his first term to designate Mexican drug cartels as terrorist groups.