At the same time, Mattis ordered a similar review of the $4 billion cost for developing a new aircraft for the US president, Air Force One, the ultra-high-tech and secure 747 built by Boeing.
"The F-35 Joint Strike Fighter programme is a critical acquisition programme that warrants a detailed assessment to reduce associated programme costs," Mattis said in the order.
He said the deputy secretary of defense will oversee the review to find ways "to significantly reduce the cost" while ensuring the new jets, which cost about $100 million each, meet US defense needs.
He said the review should also compare the F-35 with the Boeing-built F-18 Super Hornet fighter to see if the latter, which costs significantly less, can meet US needs.
In December, Trump assailed both the F-35 and Air Force One programmes as overly costly, and after that met with the chief executives of Lockheed Martin and Boeing to try to extract savings.
"The F-35 programme and cost is out of control. Billions of dollars can and will be saved on military (and other) purchases," Trump said on Twitter at the time.
- Lockheed shares sink -
The first 200 F-35s of a programme that envisions some 2,450 ultimately being acquired by the different US armed services have been delivered. The aircraft have also been sold to Israel, with the first two delivered in December.
Proponents tout the F-35's radar-dodging stealth technology, supersonic speeds, close air-support capabilities, airborne agility and a massive array of sensors giving pilots unparalleled access to information.
News of Mattis' order sent Lockheed shares tumbling. They were trading up about 1.0 percent before the announcement; dropping 1.0 percent at $252.18 afterward.
Boeing shares fell in early trade and were off 0.9 percent after the announcement.
Lockheed said in a statement that it "welcomes" Mattis's review and its focus on costs.
The company said costs can be cut if the programme adopts a multi-year procurement approach that would allow components to be bought on a large scale.
It also argued that the F-35 is the best alternative.
"We are confident such a thorough and objective analysis will show that only the F-35, with its advanced stealth and sensors, can meet the 21st century air superiority requirements of all of our military services," Lockheed said.
On Tuesday, Lockheed chief executive Marillyn Hewson sought to assuage shareholders by saying the new president's objective is not "about slashing our profits."
"We understand his concerns about affordability and we certainly share that," she said in a conference call with analysts. "It's about how do we get the costs down today and in the future."
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