Mr Trump said it would be "wonderful" if no nation had nuclear arms, but otherwise the US must be "top of the pack".
He told Reuter that the US had "fallen behind on nuclear weapon capacity".
Critics say the US and Russia already have more weapons than necessary to deter a nuclear attack.
The US has 6,800 nuclear weapons and Russia has 7,000, according to the US nonpartisan Arms Control Association.
Speaking to Reuters in a wide-ranging interview, Mr Trump said: "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, 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."
His latest comments on nuclear weapons echo a tweet he sent a few weeks after his election win, in which he pledged to increase the country's capability.
A new strategic arms limitation treaty between the US and Russia, known as New Start, requires that by 5 February of next year, both countries must limit their arsenals of strategic nuclear weapons to equal levels for 10 years.
The independent Arms Control Association non-profit group criticised Mr Trump's remarks.
"Mr Trump's comments suggest, once again, that he is ill-informed about nuclear weapons and has a poor understanding of the unique dangers of nuclear weapons," the group said in a statement.
"The history of the Cold War shows us that no one comes out on 'top of the pack' of an arms race and nuclear brinksmanship."
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