NBC News published a piece alleging that he made the ask over the summer after seeing a slide displaying the reduction in American nuclear weaponry since the 1960s.
Trump also threatened to "challenge their license," although what that would entail specifically is unclear. The Federal Communications Commission, the body that oversees licensing, didn't immediately respond to a request for comment, but its website notes that it doesn't oversee television or radio networks.
"According to the officials present, Trump's advisers, among them the Joint Chiefs of Staff and Secretary of State Rex Tillerson, were surprised," the NBC piece says. "Officials briefly explained the legal and practical impediments to a nuclear buildup and how the current military posture is stronger than it was at the height of the buildup. In interviews, they told NBC News that no such expansion is planned."
Trump's tirade against the network ramped up last week after NBC reporters nabbed a scoop claiming that Tillerson called him a "moron" and threatened to not return to Washington, D.C., while he was visiting Texas.
Tillerson ended up making on-camera remarks the same day following rumors that the piece was an indication that he planned to resign. He didn't deny having made the comment but did brush off the rumor as "petty stuff." He also reaffirmed his commitment to Trump and to the country.
Trump attacked NBC several more times over the course of the week, insisting that Tillerson never threatened to resign. NBC told HuffPost last week in a statement that it stood by its reporting.
This article has been updated with information about the Federal Communications Commission.