AP Photo/Evan Vucci
The request, which would violate decades of nuclear disarmament treaties and reverse longstanding US policy, reportedly provoked Secretary of State Rex Tillerson to call the president a "moron."
"Fake @NBCNews made up a story that I wanted a "tenfold" increase in our U.S. nuclear arsenal. Pure fiction, made up to demean. NBC = CNN!" Trump wrote.
The president suggested in another tweet that "the Networks," presumably referring to cable news, should lose their "License."
"With all of the Fake News coming out of NBC and the Networks, at what point is it appropriate to challenge their License? Bad for country!" he wrote.
Officials told NBC that Trump was presented with a chart that illustrated the decline in the size of the US nuclear arsenal, which now includes 4,000 weapons, during the Pentagon meeting. After viewing the chart, Trump asked officials present at the meeting, which included top White House aides, and cabinet and Pentagon officials, to grow the arsenal to 32,000, the number it reached at its peak in the 1960s.
NBC reported that officials were disturbed by the president's apparent lack of understanding of a range of national security and military issues amid a standoff with nuclear-armed North Korea.
Soon after this meeting, NBC's sources heard Tillerson call Trump a "moron," a remark that was reported earlier this month, prompting Tillerson to confirm his commitment to the administration and compliment the president in an impromptu news conference. Trump said he believed the report of Tillerson's insult was "fake news," but then challenged Tillerson to an IQ test during an interview with Forbes earlier this week.
"I think it's fake news," Trump told Forbes. "But if he did that, I guess we'll have to compare IQ tests."
"And I can tell you who is going to win," Trump said.
Arms-control experts maintain that an increase in US arms would spur another arms race with Russia and most likely China and could lead to other countries seeking nuclear capabilities.
But Trump has ordered the Pentagon to review its nuclear posture, with the US reassessing its nuclear assets in light of evolving threats. The most recent nuclear-posture review came in 2010 under President Barack Obama with the express goal of reducing weapons stockpiles.
Trump has voiced inconsistent opinions on the nuclear arsenal, at one point expressing a desire to "greatly strengthen and expand [US] nuclear capability," and in other instances insisting he does not think the arsenal should grow in size.
The country is embarking on a trillion-dollar modernization effort to update all three legs of its nuclear triad.
Alex Lockie contributed to this report.