Trump shared the tweet, from Fox News commentator Brit Hume, which featured an image of a masked Biden with the caption: "This might help explain why Trump doesn't like to wear a mask in public. Biden today."
The President denied that he was mocking Biden and asked why the Democratic candidate was wearing the mask while "standing outside" in "perfect conditions".
"I thought that was fine," Trump said. "I wasn't criticising him."
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Trump's campaign against masks has seen him repeatedly refuse to wear one in public, against official advice.
The President has been told he is "no longer welcome" in Michigan after refusing to wear a face mask on camera while visiting one of the state's car factories.
Under an executive order issued by Governor Gretchen Whitmer, "any individual able to medically tolerate a face covering" must wear one "when in any enclosed public space".
Last week, Trump visited Ypsilanti, Michigan, and toured a Ford plant which has been repurposed to manufacture ventilators and personal protective equipment.
When the President emerged to speak to the media, he was not wearing a mask.
• Covid19.govt.nz: The Government's official Covid-19 advisory website