The president’s family business pays at least $3 million a year to the federal government for the lease on its D.C. hotel, which is all but empty because of the virus. The next monthly payment is coming due.

The Trump International Hotel in Washington is owned and operated by the president’s family business, but the building belongs to the government.

President Trump’s signature hotel in the nation’s capital wants a break on the terms of its lease. The landlord determining the fate of the request is Mr. Trump’s own administration.

Trump International Hotel, just a few blocks from the White House, had been a favored gathering place for lobbyists, foreign dignitaries and others hoping to score points with the president. But like most hotels, it is now nearly empty and looking to cut costs because of the coronavirus pandemic.

In recent weeks, the president’s family business has inquired about changing its lease payments, according to people familiar with the matter, which the federal government has reported amount to nearly $268,000 per month.

The Trump Organization owns and operates the luxury hotel, but it is in a federally owned building on Pennsylvania Avenue. As part of its deal to open the 263-room hotel, the company signed a 60-year lease in 2013 that requires the monthly payments to the General Services Administration.

Eric Trump, the president’s son, confirmed that the company had opened a conversation about possible changes to the terms of the lease, which could include adjustments to future monthly payments. The Trump Organization has said it is current on its rent.

The younger Mr. Trump said the company was asking the G.S.A. for any relief that it might be granting other federal tenants. The president still owns the company, but his eldest sons run the day-to-day operations.