It's one of three major legislative proposals the White House is preparing ahead of Trump's address to lawmakers next week, his first speech to a joint session of Congress as President.
Trump said Wednesday that plans were nearly final for a health care measure that would replace the Affordable Care Act, and for the tax reform package that he promised on the campaign trail.
The White House said Trump was aiming to release his budget blueprint by mid-March, though officials acknowledged the document would amount to only a framework, and not a full plan, since key members of the White House team have just begun work. Mick Mulvaney, Trump's budget director, was confirmed last week.
Speaking ahead of his meeting Wednesday, Trump promised a plan that would allocate taxpayer dollars carefully, with an eye toward reducing wasteful spending.
"I want the American people to know that our budget will reflect their priorities. We'll be directing all of our departments and agencies to protect every last American and every last tax dollar. No more wasted money," Trump said at his meeting, which took place at the White House.
Attendees included his chief of staff, Reince Priebus, his chief strategist, Steve Bannon, and his senior adviser, Jared Kushner. Other members of Trump's economic team, including Mulvaney and Treasury Secretary Steven Mnuchin, also participated.
"We're going to be spending the money in a very, very careful manner," Trump told reporters. "Our moral duty to the taxpayer requires us to make our government leaner and more accountable. We must do a lot more with less. And we must stop the improper payments and the abuses, negotiate better prices and look for every last dollar of savings."
While Trump has vowed to reduce spending on some domestic programs, he's also promised projects that will require billions of dollars in new expenditures, including his proposed border wall, the cost of which has been estimated from $10-$15 billion. He's also promised a $1 trillion infrastructure plan, though precise details of that proposal have not yet been revealed.
People familiar with the budget plan have not yet revealed how the blueprint will bring down the debt. Trump has also vowed to enact widespread tax cuts, which would increase the deficit by reducing federal revenue.
The White House has already identified certain government programs that could come under the knife in the budget proposal. People familiar with the budget plan confirmed reports that a series of federal programs were being considered for major cuts in Trump's budget. The affected organizations include the Corporation for Public Broadcasting and the National Endowments for the Arts and Humanities.
At the same time, Trump has vowed to increase military spending. Vice President Mike Pence repeated that promise in Europe over the weekend on his first trip abroad since taking office.
"As we speak, the United States is developing plans for significant increases to ensure that the strongest military in the world is stronger still," Pence said during remarks at the Munich Security Conference.
A president's budget typically acts as a statement of White House priorities rather than an actual legislative vehicle. Members of Congress are responsible for drafting and passing a federal budget plan, though with Republicans in control of both chambers of Congress, this year's plan is more likely to reflect White House thinking than when President Barack Obama was in the Oval Office.
Whatever plan does emerge will face stiff Democratic resistance, particularly if it contains the type of deep cuts to domestic programs that have been promised. Increasing military spending will require Congress to eliminate mandatory spending caps that were put in place in 2011; Democrats are likely to insist that similar caps on domestic spending also be lifted.
Speaking Wednesday, Trump expressed concern at the size of the federal debt, but also seemed to downplay expectations for what long-term analyses of his budget might show.
"In all fairness, I've only been here for four weeks, so I can't take too much of the blame for what's happened," Trump said. "But it is absolutely out of control, and we're going to do things that are going to be tremendous over the years."
He added: "We have enormous work to do as the national debt doubled over the last eight years. Our debt has doubled over a short period of time."
Trump hasn't always been troubled by debt, though. He once termed himself "the king of debt" when discussing his private business empire.