Critics argued a parade could cost millions of dollars, at a time the Pentagon wants more stable funding for an overstretched military.
"A military parade in D.C. would shut down the nation's capital and waste taxpayer dollars just to feed Trump's ego," said Eleanor Holmes Norton, a non-voting delegate to the U.S. Congress for the District of Columbia, a Democratic stronghold.
U.S. Senator Lindsey Graham, a prominent Republican voice on defence matters, said he favoured highlighting the country's armed forces but not its weaponry.
"I think a parade showcasing the military and the sacrifices they make for the country would be appropriate, it would be a way to say thank you, but I'm not interested in a military hardware display. That would be cheesy and project weakness," Graham told reporters on Wednesday.
The White House said on Tuesday it had asked the Pentagon to explore a celebration of "America's great service members," after the Republican president marvelled at the Bastille Day military parade he attended in Paris last year.
Defense Secretary Jim Mattis - who argued to lawmakers on Tuesday that a budgetary impasse was eroding U.S. advantages over adversaries and could lead to aircraft being grounded - said the Pentagon was putting together options that would be sent to the White House.
"I think we're all aware in this country of the president's affection and respect for the military," Mattis told reporters, while declining to address the costs of the parade.
One option under consideration is for a parade on Nov. 11 - which would be the 100th anniversary of the end of World War One.
Military parades in the United States are generally rare. Such parades in other countries are usually staged to celebrate victories in battle or showcase military might.
That parade cost $12 million, according to a report at the time. While the Pentagon does not yet have a cost estimate for how much another parade may cost, it is likely to be in the millions of dollars. U.S. officials say it would also be a logistical challenge to bring thousands of troops, tanks and aircraft to Washington.
The District of Columbia Council ridiculed the idea of a parade on Pennsylvania Avenue, the 1.2-mile (1.9-km) stretch between the Capitol and the White House that is also the site of the Trump International Hotel.
"Tanks but no tanks!" it tweeted.
Washington Mayor Muriel Bowser's spokeswoman said the District had no formal request for a parade but "just like the wall, he will have to pay for it," a reference to Trump's plan to build a wall on the U.S.-Mexico border and have Mexico pay for it. The Mexican government has insisted it will not do so.
Trump publicly expressed his interest in an American military display after watching the Paris parade.
The July 14 military parade has been seen as an opportunity for France's armed forces to present themselves to the French people. The parade included 63 planes and nearly 4,000 troops.
The cost ranged between $4.3 million (3.5 million euros) to $4.9 million (4 million euros), which comes out of the French defence budget.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)
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