After the meeting, both the CEOs Dennis Muilenburg of Boeing and Marillyn Hewson of Lockheed appeared to have addressed the concerns of the President-elect.
"We're going to get it done for less than that (USD 4 billion), and we're committed to working together to make sure that happens," Muilenburg told reporters after his meeting with Trump at Mar-a-Lago estate in Florida.
He was responding to a question on Trump's criticism of Boeing manufacturing Air-Force One at an exorbitant cost.
In a statement, Hewson said he had a productive meeting with Trump.
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"I appreciated the opportunity to discuss the importance of the F-35 program and the progress we've made in bringing the costs down. The F-35 is a critical programme to our national security, and I conveyed our continued commitment to delivering an affordable aircraft to our US military and our allies," he said.
The Boeing CEO said the meeting went great.
"Very productive, and really encouraged by the dialogue. Good, open discussion. And we're all focused on the same thing here, we're going to make sure that we give our warfighters the best capability in the world and that we do it in a way that is affordable for our taxpayers," he said.
Muilenburg said he and Trump talked about Air Force One.
Boeing, he said is working with the White House on its timeline.
"We have an active 747 production line and we're eager to get started on the programme. We haven't actually started the build of the airplane yet, but once we finalise the requirements and make sure that it's affordable we'll launch on building the aircraft. We've got a hot production line and we're ready to go," Muilenburg said.
"Trying to bring costs down-costs. Primarily the F-35, trying to get the costs down. A programme that is very, very expensive," Trump told reporters in response to a question.
Asked whether he secured any concessions from Hewson.
"We're just beginning, it's a dance. It's a little bit of a dance. But we're going to get the costs down and we're going to get it done beautifully," he said.
Trump also met with a group of senior Pentagon officials.