Mr Trump also maintained that face coverings do not need to become mandatory to curb Covid-19's spread.
He again predicted the infection would "disappear," as the US hit a new record high of 52,000 virus cases in a day.
His remarks to Fox News come a day after a top Republican called on Mr Trump to wear a mask as an example.
The US now has nearly 2.7 million confirmed Covid-19 infections and more than 128,000 deaths, according to Johns Hopkins University, which is tracking the pandemic.
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