Mr Trump said it would allow the US to stay at the “top of the pack” and expressed concern that America has "fallen behind on nuclear weapon capacity”.
He also hinted at a change of course from Washington on America’s involvement in a new strategic arms limitation treaty.
Repeating a phrase often used by the President to criticise trade pacts, the former property tycoon said the latest non-proliferation arrangement was a “one-sided deal”.
Under the treaty, known as New Start, by February 2018 the US and Russia must limit their arsenals of strategic nuclear weapons to equal levels for 10 years.
It also permits both countries to have no more than 800 deployed and non-deployed land-based intercontinental and submarine-launched ballistic missile launchers and heavy bombers equipped to carry nuclear weapons.
But Mr Trump said: "Just another bad deal that the country made, whether it's Start, whether it's the Iran deal... We're going to start making good deals.”
“I am the first one that would like to see everybody - nobody have nukes, but we’re never going to fall behind any country even if it’s a friendly country,” he added.
“We’re never going to fall behind on nuclear power.
"It would be wonderful, a dream would be that no country would have nukes, but if countries are going to have nukes, we’re going to be at the top of the pack.”
Speaking from the Oval Office, he told Reuters he was “very angry" at North Korea's ballistic missile tests and said accelerating a missile defence system in the region was among many options available to him.
The comments are the new US President’s first on the issue of America’s nuclear arsenal.
Barack Obama made reducing the world’s nuclear weapons stockpile a priority during his eight years in office.
In a major speech just a few months after his inauguration in 2009, Mr Obama declared his “commitment to seek the peace and security of a world without nuclear weapons”.
Additional reporting Reuters
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