It is one more example of how Trump is insisting that his initiatives to beautify the White House and the city are also serving a defensive purpose.
Trump has been calling the new White House ballroom a "military complex" and arguing it is necessary for national security purposes.
The Pentagon said it had no information beyond the president's statement.
Trump's announcement also comes as the arch, like his other projects, faces legal challenges.
Though the arch has received early approval from the US Commission of Fine Arts, whose members were all tapped by Trump, a group of three veterans and an architectural historian sued, saying the project needs to be approved by Congress.
"The President's belated efforts to manufacture a national security justification for this project do nothing to cure its fundamental illegality," Nicolas Sansone, one of the lawyers representing the litigants, said on Sunday.
"Congress has not authorised the arch and unless and until Congress does so, the project should not be permitted to move forward."
Trump said in a social media post that he had agreed, at the "strong request" of the military, to convert the planned 250-foot-tall (76-metre) memorial arch "into a top grade Military Complex/Triumphal Arch, to house, store, and have the rapid ability to use large numbers of drones, plus Snipers, on both the roof and plaza areas, and additionally have and hold large quantities of sniper ammunition in storage."
The arch is proposed for a circle adjacent to the Memorial Bridge, which is a heavy traffic area as one of a handful of connecting bridges between the nation's capital and northern Virginia.
The project is one of several the president is pursuing to leave his lasting imprint on Washington.
Among the others are the White House ballroom, renaming and renovating the Kennedy Center, refurbishing the Lincoln Memorial Reflecting Pool and rebuilding a golf course in East Potomac Park, which could significantly reduce the public's access to running and biking paths.
The arch has not yet received final approval from the National Capital Planning Commission, which greenlit the site and preliminary plans at its July meeting.
