The head of Lockheed Martin has promised to “aggressively” drive down the cost of the F-35 fighter jet after Donald Trump criticised the price of the defence project on Twitter.

Mr Trump suggested an older aircraft made by rival aerospace company Boeing could offer a cheaper alternative to the F-35, said to be the world’s most expensive weapons program.

“Based on the tremendous cost and cost overruns of the Lockheed Martin F-35, I have asked Boeing to price-out a comparable F-18 Super Hornet!” he wrote in a tweet.

Marillyn Hewson, Lockheed Martin’s CEO, told the President-elect she was personally committed to reducing the cost of the F-35 and had heard his message “loud and clear”.

In a statement, said she had had “a very good conversation” with Mr Trump.

“I gave him my personal commitment to drive the cost down aggressively,” she said.

Lockheed Martin’s stocks took a tumble following the tweet, the latest in an ongoing war of words between the President-elect and US defence companies, which he has criticised for excessive costs.

An F35 fighter jet. Donald Trump said the 'F35 program and cost is out of control'. (Getty)

The company’s shares fell by around 2 per cent following Mr Trump’s comments, nearing their lowest levels since the Presidential election.

This is the second time the President-elect has sparked a Lockheed Martin stock wobble of millions this month.

Mr Trump, who takes office on 20 January, has promised to cut government procurement costs as part of his industrial policy.

“The F-35 program and cost is out of control. Billions of dollars can and will be saved on military (and other) purchases after January 20th,” tweeted Mr Trump on 12 December – causing the company’s market value to fall by $3.5bn, which it later recovered.

Mr Trump met Ms Hewson and Boeing head Dennis Muilenburg this week at his seafront Mar-a-Lago estate in Florida.

The President-elect has also used the bully pulpit to cause Boeing’s stock to fall when he said costs for a project to build two new Air Force One planes were “out of control”.

“Boeing is building a brand new 747 Air Force One for future presidents, but costs are out of control, more than $4 billion. Cancel order!” tweeted Mr Trump, causing a temporary dip of Boeing’s stock of around $2 a share.

Mr Muilenburg said he had promised Mr Trump the manufacturer would complete the Air Force One project for less than the $4bn the president-elect claimed it would cost.

Ms Hewson did not speak to reporters after her meeting with Mr Trump but released a statement which said it had been “productive”.

“I appreciated the opportunity to discuss the importance of the F-35 program and the progress we've made in bringing the costs down,” she said.

“The F-35 is a critical program to our national security, and I conveyed our continued commitment to delivering an affordable aircraft to our U.S. military and our allies.”

Mr Trump told reporters the focus of his meetings had been to try and reduce the costs of the programs, according to Reuters.

“Primarily the F-35, we're trying to get the cost down. It's a program that's very, very expensive.“

Of his meeting with Ms Hewson, the President-elect said: “It's a little bit of a dance. We're trying to get costs down.”

Women go on strike against Donald Trump Show all 7 1 /7 Women go on strike against Donald Trump Women go on strike against Donald Trump People rally as part of a nationwide protest against US President-elect Donald Trump outside of Trump Tower on December 12, 2016 in New York. Timothy A Clary/AFP/Getty Images Women go on strike against Donald Trump Protestors march during a demonstration against U.S. President-elect Donald Trump near Trump Tower in the Manhattan borough of New York City, December 12, 2016. Shannon Stapleton/Reuters Women go on strike against Donald Trump Protestors march during a demonstration against U.S. President-elect Donald Trump near Trump Tower in the Manhattan borough of New York City, December 12, 2016. Shannon Stapleton/Reuters Women go on strike against Donald Trump People rally as part of a nationwide protest against US President-elect Donald Trump outside of Trump Tower on December 12, 2016 in New York. Timothy A Clary/AFP/Getty Images Women go on strike against Donald Trump People rally as part of a nationwide protest against US President-elect Donald Trump outside of Trump Tower on December 12, 2016 in New York. Timothy A Clary/AFP/Getty Images Women go on strike against Donald Trump People rally as part of a nationwide protest against US President-elect Donald Trump outside of Trump Tower on December 12, 2016 in New York. Timothy A Clary/AFP/Getty Images Women go on strike against Donald Trump People rally as part of a nationwide protest against US President-elect Donald Trump outside of Trump Tower on December 12, 2016 in New York. Timothy A Clary/AFP/Getty Images

Boeing's F-18 is an older generation aircraft that lacks the stealth capabilities of the F-35.

One US official said it was impossible to tell what Trump meant by his tweet, given the importance of stealth technology as a way to counter advanced defenses of near-peer states, like Russia or China.

“Somebody needs to ask Donald Trump how he's going to be able to confront China without aircraft capable of penetrating anti-access and area denial systems, including air defenses,” the official said.