Officials from President Donald Trump's administration estimated during a congressional briefing this week that the first six days of the war on Iran had cost the United States at least $11.3 billion, a source familiar with the matter said on Wednesday.

That figure, from a closed-door briefing for senators on Tuesday, did not include the entire cost of the war, but was provided to lawmakers as they have clamored for more information about the conflict.

Several congressional aides have said they expect the White House to soon submit a request to Congress for additional funding for the war.

Some officials have said the request could be for $50 billion, while others have said that estimate seems low.

The administration has not provided a public assessment of the cost of the conflict or a clear idea of its expected duration.

Trump said during a trip to Kentucky on Wednesday that "we won" the war but that the United States would stay in the fight to finish the job.

The $11.3 billion figure was first reported on Wednesday by the New York Times.

The campaign against Iran began on Feb. 28 with U.S. and Israeli air strikes and has so far killed around 2,000 people, mostly Iranians and Lebanese, as the conflict has spread into Lebanon and thrown global energy markets and transport into disarray.

Administration officials also have told lawmakers that $5.6 billion of munitions was used during the first two days of strikes.

Some critics in Congress have expressed concern that the conflict will deplete U.S. military stocks at a time when the defense industry is said to be struggling to keep up with demand.

Trump met executives from seven defense contractors last week as the Pentagon worked to replenish supplies.

Democrat lawmakers have demanded public testimony under oath from administration officials about the Republican president's plans for the war, including how long it might last and what his plans are for Iran once the fighting has stopped.

Among other things, Trump has said he wants to be involved in the selection of a new Iranian leader.