Boeing CEO Dennis Muilenburg — whose company is under contract with the US Air Force to develop and manufacture the next presidential aircraft fleet — said the price will be less than a near-$4 billion estimate.

"We're going to get it done for less than that, and we're committed to working together to make sure that happens," Muilenburg said after meeting at Trump's Mar-a-Lago resort in Palm Beach, Florida.

"I was able to give the president-elect my personal commitment on behalf of the Boeing Company. This is a business that's important to us. We work on Air Force One because it's important to our country and we're going to make sure that he gets the best capability and that it's done affordably."

Trump described the cost for Boeing's Air Force contract to develop the next presidential fleet as "out of control" in a December 6 tweet.

"The $4 billion is a theoretical estimate of the life of the program, which is approximately 30 years," a Department of Defense spokesman told Business Insider.

Considering the US Air Force contract with Boeing is in very early stages, it is entirely possible for that figure to be adjusted, the spokesman added.

Trump also met with Lockheed Martin CEO Marillyn Hewson on Wednesday.

On December 12, Trump said the cost for Lockheed Martin's fifth-generation stealth F-35 Lightning II jet was also "out of control."

The message sent Lockheed Martin's stock down from $251 at the opening bell to $245.50, before it rebounded to a little more than $253 a share.

"We're trying to get costs down ... primarily the F-35, we're trying to get the cost down. It's a program that is very, very expensive," Trump said after meeting with several generals and admirals on Wednesday.

Trump said the negotiations with Lockheed Martin were "just beginning" and described it as "a little bit of a dance."

The F-35, valued at an acquisition cost of $379 billion, has become one of the most challenged programs in the history of the Department of Defense. It has experienced setbacks that include faulty ejection seats, software delays, and helmet-display issues.

"This program is not out of control," Lt. Gen. Chris Bogdan, head of the F-35 Joint Program Office, said during a December 19 briefing with reporters, just days after Trump tweeted criticism of the program.

"If given the opportunity I would like to try and explain to the new administration that this is a vastly different program from 2011," Bogdan said. "I'll just lay the facts out on the table and I'll let them make their own judgments because I don't think the program cost wise is out of control nor do I think that it's out of control schedule wise."