During the press briefing, Mr Trump criticised his Democratic presidential opponent, Joe Biden, and touted the recovery of the US economy amid the Covid-19 pandemic, before inviting questions from the media.
Mr Trump called on Jeff Mason, a Reuters reporter and former president of the White House Correspondents’ Association, who began to ask his question.
But he was immediately cut off by the president who complained of his "muffled" speech, saying: "You're going to have to take that [the mask] off, please. You can take it off. How many feet are you away?"
Mr Mason refused to remove his face covering and instead offered to speak louder, before the president cut back in, saying: "Well, if you don't take it off, you're very muffled, so if you would take it off, it would be a lot easier."
The reporter, however, stood his ground and slightly raised his voice, before asking: "Is that better?" to which a visibly annoyed president rolled his eyes and replied: "It's... better, yeah."
Other reporters present at the briefing did remove their masks when asking questions. "You sound so clear, as opposed to everybody else,” Mr Trump sarcastically told one journalist, who did remove their face covering while speaking.
The White House Correspondents’ Association, which Mr Mason now serves as vice president after a stint as president from 2016-17, asks its members to wear face coverings while reporting during the coronavirus pandemic.
Monday's testy exchange was not the first time the president and Mr Mason locked horns at a White House media briefing. At a Rose Garden press conference back in May, Mr Trump accused Mr Mason of "wanting to be politically correct" for not taking off his mask while speaking.
At that same press conference, the president had been forced to deny claims that he mocked Joe Biden for wearing a face mask to an outdoor Memorial Day event.
Mr Biden and his wife Jill wore black face coverings at the event in Delaware, while the president and his wife Melania chose not to while attending a similar Memorial Day services in Baltimore and Arlington, Virginia.
Mr Trump had until July refused to wear a face covering, despite the US being the worst hit country in the world in terms of coronavirus deaths and infections.
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