The tweet was one in a series from Trump in which he criticized the network for a story it published Wednesday stating he wanted to increase the U.S. nuclear arsenal by almost tenfold.
Mr. Trump said that NBC News' reporting is "Pure fiction, made up to demean" and compared it to CNN, which he has previously also criticized and labeled as "fake news".
The President's denial was buttressed by a statement from his defence chief.
Trump's "comments raised questions about his familiarity with the nuclear posture and other issues".
NBC News has incurred the wrath of Trump's ire in recent days after a report last week Tillerson called the president a "moron" and almost resigned.
"Fake @NBCNews made up a story that I wanted a "tenfold" increase in our USA nuclear arsenal", Trump wrote. Trump denied the story and suggested the Senate Intelligence Committee investigate "the fake news networks". "This kind of erroneous reporting is irresponsible", Defence Secretary Jim Mattis said.
"The whole point of the First Amendment is to make sure the government can't stop speech before it happened and the government can't censor speech because it disagrees with what that speech says".
According to the report, Trump asked for "what amounted to a almost tenfold increase" after being presented with a graph that showed a gradual reduction in nuclear weapons since the 1960s.
During a joint meeting with Canadian Prime Minsiter Justin Trudeau at the White House Trump said that the current nuclear arsenal of the United States is already sufficient, and that no increase is needed.
The initial report about Tillerson's comment prompted Tillerson to confirm his commitment to the administration and compliment the president in an impromptu news conference.
During an address to the United Nations General Assembly in September, Mr Trump declared that the U.S. would "totally destroy North Korea" if forced to defend itself or its allies.
"Trump indicated he wanted a bigger stockpile, not the bottom position on that downward-sloping curve", NBC News reported, adding that those present were surprised by the request.