In a motion filed on Friday, US government lawyers say that the federal judge's order to suspend construction of the new facility is "threatening grave national-security harms to the White House, the President and his family, and the President's staff".
"Time is of the essence!" the lawyers write, citing materials that will be installed to make a "heavily fortified" facility.
The ballroom is part of President Donald Trump's plans to quickly remake Washington.
US District Judge Richard Leon in Washington on Tuesday ordered the temporary pause of the construction project that included demolishing the East Wing of the White House.
He concluded that unless Congress approves the project, the preservationist group suing to stop it is likely to succeed on the merits of its claims because "no statute comes close to giving the president the authority he claims to have".
The judge suspended enforcement of his order for 14 days, acknowledging that the administration would appeal his decision.
Leon's ruling and the appeal came the same week a key agency tasked with approving construction on federal property in the Washington region gave final approval to the project.
In his ruling, Leon, who was nominated by Republican President George W Bush, suspended enforcement of his order recognising that "halting an ongoing construction project may raise logistical issues".
Leon also addressed national security in his ruling, saying that he reviewed information that the government privately submitted to him and concluded that halting construction wouldn't jeopardise national security.
He exempted any construction work that is necessary for the safety and security of the White House from the scope of the injunction.
Trump lashed out at the ruling, but also noted that it would allow work on underground bunkers and other security measures around the White House grounds to continue — even though those will be paid for by taxpayers.
Trump has pledged that he, along with private donors, will cover the costs for the ballroom construction.
But government lawyers argue that the president has "complete authority to renovate the White House" and the current state of the grounds, which is an open construction site, makes it harder to protect the White House.
"Canvas tents, which are necessary without a ballroom, are significantly more vulnerable to missiles, drones, and other threats than a hardened national security facility," the motion says.
The Trump administration is asking the appeals court to make a decision on its request by Friday.
It also asked that the 14-day suspension of Leon's order be extended by another two weeks so that the case can be taken to the Supreme Court.
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