The Pentagon said in a memo on Friday that the reviews were to "inform programmatic and budgetary decisions, recognizing the critical importance of each of these acquisition programs."
"The Deputy Secretary of Defense shall oversee a review of the F-35 program to determine opportunities to significantly reduce the cost of the F-35 program while meeting requirements," the Pentagon said in a statement.
In a statement on Friday, Lockheed Martin said it "stands ready to support Secretary Mattis' review of the F-35 program and welcomes the appropriate focus on affordability and capability. "
"We also believe there are opportunities to continue to drive down program costs by using sound buying practices such as multi-year procurement that enable the Government to purchase thousands of critical components at an economic scale," The company added.
Since his Nov. 8 election victory, President Donald Trump has been critical of both companies. Last year, Trump took a shot at Boeing, threatening to cancel the order for a new 747 Air Force One program, and he criticized the Lockheed program's delays and costs.
Earlier this month, Lockheed Martin CEO Marillyn Hewson said the defensive contractor is "close to a deal" to bring down the cost of its F-35 fighter program following repeated criticisms from Trump.
The reviews should begin immediately, according to the memo.
Shares of Lockheed Martin ended the day about 0.6 percent lower, while Boeing shares fell 0.8 percent.