NBC News said the president called for the increase after he was shown a chart indicating the stockpile of U.S. nuclear weapons had slid from a high of 32,000 in the 1960s. Trump said he wanted to have that same number now, NBC reported.
Speaking to reporters at the White House during a meeting with Canadian Prime Minister Justin Trudeau, Trump said the report was not true.
"I never discussed increasing it. I want it in perfect shape. That was just fake news by NBC," he said. "We don't need an increase. But I want modernisation and I want total rehabilitation. It's got to be in tip-top shape."
The president's denial was buttressed by a statement from his defence chief.
"Recent reports that the president called for an increase in the U.S. nuclear arsenal are absolutely false. This kind of erroneous reporting is irresponsible," Defense Secretary Jim Mattis said.
Although U.S. presidents have modernised weapon stockpiles over the years, any meaningful addition to the nuclear arsenal would violate treaty agreements. The Federation of American Scientists says the United States currently has about 4,000 nuclear warheads earmarked for use in its military stockpile.
The NBC report comes during a time of high tension between the United States and North Korea over Pyongyang's nuclear weapons and missile programs, and just ahead of an expected announcement from Trump on whether to decertify the international deal on Iran's nuclear programme.
Trump told Reuters in February that he wanted to ensure that the U.S. nuclear arsenal was at the "top of the pack."
MSNBC reported in 2016 that as a candidate, Trump asked a foreign policy adviser three times in a one-hour meeting why the United States could not deploy its nuclear weapons.