Lockheed Martin is close to winning the orders it needs to rapidly produce the F-35 fighter, the most expensive weapons system in U.S. history.

The aircraft maker is nearing a deal worth between $35 billion and $40 billion to supply 440 F-35 Lightning II Joint Strike Fighter jets to the United States and 10 allied nations over the next several years, Lockheed (LMT) executive Jeff Babione said on Monday at the Paris Air Show.

"This more than doubles the total amount of airplanes under contract, and that we'll be building," Babione said of the agreement with governments to ramp up production of the world's most sophisticated fighter jet.

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The deal promises big economic benefits. It would secure jobs at Lockheed and international partner factories in Texas, Italy and Japan, where more than 140 jets are now in production. The deal would support about 150,000 jobs worldwide connected to the program and a projected 200,000 jobs that eventually would be added, Babione said.

If concluded, the agreement would bring much needed relief to Lockheed's troubled program, which carries an estimated total cost of $400 billion. The company has been under pressure from President Trump to lower the price tag of each individual plane.

Trump has made no secret about his dislike for expensive government aircraft programs. In April, he touted his prowess as a negotiator and promised to save money on the expensive F-35. His comments followed a statement from Lockheed in February that credited Trump for helping to accelerate negotiations.

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"This was a thing that was out of control and now it's great," President Trump said at the time. Trump was given credit by Lockheed executives for securing a lower price on the most recent deal, but estimates by Pentagon officials prior to Trump's election victory closely match the agreed price.

The proposed deal includes all three variations of the sophisticated fifth generation stealth fighter, including the F-35 B variant -- which is able to hover -- for the U.S. Marine Corps and U.K's Royal Navy.

Falling cost per plane

The cost of each F-35 has now dipped below $95 million, Lockheed said Monday. The company hopes to eventually get that down to $85 million in a few years.

The news emerged at the Paris Air Show, a gigantic aviation industry event at which aircraft makers show off their new planes to potential buyers. Itt's a welcome change for supporters of the F-35, who've endured a series of recent disappointments.

A unit of the jets at Luke Air Force Base was grounded after pilots reported problems with cockpit oxygen systems.

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In April, a report from the congressional Government Accountability Office watchdog group recommended that the Pentagon refrain from making "significant new investments" in the fighter jet until the entire testing process is finished.

Testing is now 90% complete. Full rate production of the aircraft, which is scheduled for April 2019, could cost the U.S. Department of Defense more than a billion dollars more than what was budgeted in 2011 when the program was restructured.

The F-35 is the nation's most sophisticated fighter jet, outfitted with stealth technology and a cockpit helmet display that allows pilots to virtually see through the airplane at targets on the ground below.

-- CNN's Zachary Cohen and Ryan Browne contributed to this report.