"It's frankly disgusting the way the press is able to write whatever they want to write, and people should want to look into it," Trump fumed as he met his Canadian counterpart in the Oval Office.
But the president -- who has a history of being combative with the media -- said he did not want to see formal restrictions.
"No. The press should speak more honestly, I mean, I've seen tremendously dishonest press. It's not even a question of distortion."
His secretary of defense backed him publicly.
"Recent reports that the president called for an increase in the US nuclear arsenal are absolutely false," Pentagon chief Jim Mattis said in a statement.
"This kind of erroneous reporting is irresponsible."
The US television network reported that Trump told generals and security aides over the summer that he wanted a "nearly tenfold increase" in the US nuclear arsenal.
"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!" Trump tweeted.
Citing three officials who were in the room, NBC said Trump's response came when he was shown a slide showing the steady reduction of nukes since the 1960s.
After the briefing, the secretary of state is alleged to have called Trump a "moron," although Rex Tillerson's spokeswoman has denied that allegation.
Trump denied requesting more weapons. "I never discussed increasing it. I want it in perfect shape. That was fake news," he said.
Such a move would abrogate key international arms control treaties and upend decades of non-proliferation policy, with deep ramifications across the globe.
As president and candidate, Trump has often mused aloud about America's nuclear weapons power, saying there is no point in having them if you do not use them.
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