White House and military officials confirmed preliminary planning was already underway, but said a date had not yet been decided.
"I think we're all aware, in this country, of the president's affection and respect for the military," said Defense Secretary James Mattis.
"We've been putting together some options. We'll send them up to the White House for a decision."
Democratic lawmakers leaped to pillory Trump's plan as an "idiot" and "authoritarian" idea from a "Napoleon in the making."
Meanwhile support was thin on the ground, even among Trump's advocates in Congress.
Republican Senator Lindsey Graham told reporters on Capitol Hill that a parade "makes sense," with some caveats.
"I'm not looking for a Soviet-style hardware display. That's not who we are. It's kind of cheesy, and I think shows weakness quite frankly," he said.
"But have a parade where we can display our finest and we can all say 'thank you' and honor them would be fine."
Republican congressman Jim Jordan, a top Trump ally, suggested further deliberation was needed. "We'll have that debate," he said.
Fireworks and hotdogs
While military parades are a highlight of the calendar in Moscow, Pyongyang and Paris, they are rare in the United States, where displays of patriotism usually take the form of flag-waving, fireworks and grilled hotdogs.
The last major parade in Washington was in 1991 after the Gulf War, when missiles and tanks rolled through the streets of the capital.
As commander-in-chief, Trump could order the military to carry out a parade without any further debate.
But in a sign of possible tensions between Trump and his own staff, White House officials stressed the idea was still in "discussion."
"We haven't made a final decision," said press secretary Sarah Sanders. "We are simply exploring options."
Trump's parade might be a showcase of American muscle, but would also undoubtedly focus on his role as commander-in-chief.
Since taking office, Trump has frequently touted his support for the US military and placed high-ranking generals in top White House and Cabinet posts.
Even before being president he had mulled the possibility of a parade for his inauguration in January 2017, but the plan was scrapped.
The idea appears to have been rekindled when Trump visited Paris last July for Bastille Day, when the 45th president made no secret of his awe for the pomp and ceremony of the occasion.
Sitting on the Champs-Elysees, Trump marveled at the Republican Guard on horseback, jets flying overhead, and warmly greeted President Emmanuel Macron, who arrived in an open-topped camouflaged military jeep.
Months after that meeting, Trump publicly remarked: "So we're actually thinking about Fourth of July, Pennsylvania Avenue, having a really great parade to show our military strength."
Sanders said Trump's intention was to have "a celebration" of the military.
Still, Trump's request immediately fueled comparisons to similar events in autocratic countries.
Democratic congressman Keith Ellison described it as "the Exalted Leader's latest idiot (and authoritarian) idea."
"We have a Napoleon in the making here," said congresswoman Jackie Speier.
Republican Senator John Kennedy also piled on: "I don't think it's a particularly good idea. Confidence is silent. Insecurities are loud."
'Cadet Bone Spurs'
Trump has already prompted fears about his respect for democratic freedoms once this week by suggesting Democrats were "un-American" and "treasonous" for not applauding his recent State of the Union address.
The White House said Trump was "clearly joking."
"But what isn't a joke is that Democrats refuse to celebrate the accomplishments of last year that have helped all Americans," added Sanders.
The quip did not go down well with lawmakers, both Republicans and Democrats.
"I have seen the president's most ardent defenders use the now-weary argument that the president's comments were meant as a joke, just sarcasm, only tongue in cheek," said Republican Senator Jeff Flake.
"But treason is not a punchline, Mr President."
Military veteran and Democratic Senator Tammy Duckworth also fired back at Trump, lampooning his medical deferments from service during the Vietnam War.
"We don't live in a dictatorship or a monarchy," she said.
"I swore an oath -- in the military and in the Senate -- to preserve, protect and defend the Constitution of the United States, not to mindlessly cater to the whims of Cadet Bone Spurs and clap when he demands I clap."
