Council Member Charles Allen took to Twitter as well with a direct shot at Trump, writing, "Military parade down the streets of DC to feed an insecure man's fragile ego?" A similar parade was also held in New York City.
"It is not in the culture of the United States military - that is not who we are. there shouldn't be, in my view, a whole lot of chest-thumping and these over means of showing how tough you are".
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The Post report said a January 18 meeting between Mr Trump, Mr Mattis and senior generals at the Pentagon marked a tipping point in the president's push for a parade. CNN cited sources with knowledge of North Korea's plans saying that the reclusive country planned to show off their strength by showcasing their missiles.
The move has attracted criticism from some in the USA, with retired Major General Paul Eaton saying it underscores Trump's "authoritarian tendencies" and any parade would be about honouring Trump, not the military. There's no place quite like the Champs-Élysées, especially on a sun-splashed morning commemorating Bastille Day.
The president's reference was to a parade he saw previous year with French President Emmanuel Macron on Bastille Day.
France commits to boosting defense spending by 35 percent over six years
French Alphajets of the Patrouille de France fly over the Pyramid of the Louvre Museum during the annual Bastille Day military parade in Paris, France, on July 14, 2017. But as The Washington Post reported on Tuesday, Trump was not exaggerating his commitment.
Trump was French President Emmanuel Macron's personal guest at the event that sparked the idea.
Trump wants an elaborate parade, with soldiers marching and tanks rolling, but no date has been selected.
"The marching orders were: I want a parade like the one in France", a military official said.
"I think we're all aware in this country of the president's affection and respect for the military", Mattis said.
Trump told Macron, who was seated next to him, "We're going to have to try to top it".
The president made the request of top military chiefs in late January, after reportedly being impressed by a French Bastille Day parade a year ago.