The president also berated protesters who toppled monuments of United States leaders at recent anti-racism protests.
"There have always been those who seek to lie about the past in order to gain power in the present, those that are lying about our history, those who want us to be ashamed of who we are", Trump said on Saturday.
Trump's Fourth of July remarks doubled down on a Friday night speech at Mount Rushmore in South Dakota where he accused "angry mobs" of trying to erase history and used the speech to paint himself as a bulwark against left-wing extremism. "Their goal is demolition". Crowds on the Mall were light Saturday as officials urged social distancing, TV station WTOP reported. "That's what scientists are saying".
Florida on Saturday marked a new daily high in confirmed virus cases at 11,458 - far more than any other state.
Health officials have been bracing for a new spike in virus cases after this weekend, which they see as a potential tipping point for more infections.
His comments were followed by a military flyover involving various aircraft, including B-52 bombers and F-35 fighter jets.
Millions of Americans have been demonstrating against police brutality and racial inequality since the May 25 killing of George Floyd, a 46-year-old Black man who died after a white Minneapolis police officer knelt on his neck for almost nine minutes.
What else did Trump say?
Mr Trump said the U.S. has now tested nearly 40 million people for coronavirus, and added: "By so doing, we show cases - 99% of which are totally harmless".
Mr Trump, who faces re-election this year and appears keen to fire up his conservative base with appeals to nationalism, accused China of trying to hide the virus outbreak - a charge Beijing denies.
"China's secrecy, deceptions and cover-up allowed it to spread all over the world - 189 countries", he added.
Popular beaches on both coasts - normally packed on July 4th - were closed as California and Florida suffer alarming surges in COVID-19 infections, and Los Angeles Mayor Eric Garcetti warned citizens to "assume everyone around you is infectious".
Joe Biden, the Democratic Party rival to Mr Trump in this year's presidential election, tweeted that "this Fourth of July, one of the most patriotic things you can do is wear a mask".
Major League Baseball cancelled its 2020 All-Star Game for the first time since World War Two.