President Donald Trump doubled down on his ban of the Associated Press from key White House spaces, saying the news organization would be denied access until they refer to the body of water previously known as the Gulf of Mexico as the Gulf of America.

"We are gonna keep them out until such time that they agree that it's the Gulf of America," Trump told reporters at a Mar-a-Lago press conference on Tuesday. "We're very proud of this country, and we want it to be the Gulf of America."

"The Associated Press just refuses to go with what the law is and what has taken place," the president said, referring to an executive order he signed earlier this month that changed the gulf's name.

"I have the right to do it," he added.

The body of water's previous name is recognized by other countries and many of the AP's readers, and the outlet's policy is to refer to it on first reference as the Gulf of Mexico.

In its most recent statement on the situation, the AP said "the actions taken to restrict AP's coverage of presidential events because of how we refer to a geographic location chip away at this important right enshrined in the U.S. Constitution for all Americans."

The White House Correspondents' Association and a number of press freedom groups have slammed the Trump administration's decision and urged it to reconsider the hard-line stance.

Trump seemed to confirm that his administration and the AP were at an impasse over the donnybrook, which began Feb. 11 with the blocking of two AP reporters from two separate White House events.

"They're doing us no favors, and I guess I'm not doing them any favors," Trump said of the AP. "That's the way life works."

White House press secretary Karoline Leavitt commented on the exclusion of AP reporters during a press briefing last week, saying she wanted to "set the record straight."

"Nobody has the right to go into the Oval Office and ask the president of the United States questions," Leavitt said. "That's an invitation that is given, and there are hundreds of outlets on this campus, many of you in this room, who don't have the privilege of being part of that pool every single day and getting to ask the president questions. We reserve the right to decide who gets to go into the Oval Office, and you all have credentials to be here, including the Associated Press, who is in this briefing room today."

Leavitt also said that she was "very upfront" in her first press briefing that "if we feel that there are lies being pushed by outlets in this room, we are going to hold those lies accountable."

"It is a fact that the body of water off the coast of Louisiana is called the Gulf of America, and I'm not sure why news outlets don't want to call it that but that is what it is," she said. "The secretary of Interior has made that the official designation in the geographical identification name server. Apple has recognized that, Google has recognized that, pretty much every other outlet in this room has recognized that body of water as the Gulf of America, and it's very important to this administration that we get that right, not just for people here at home but also for the rest of the world."

• AP Reporter and Photographer Barred From Air Force One Over 'Gulf of Mexico' Terminology Dispute
• White House Bans AP From 'Limited Space' Events