In a Reuters interview, Trump also said China could solve the national security challenge posed by North Korea "very easily if they want to," ratcheting up pressure on Beijing to exert more influence to rein in Pyongyang's increasingly bellicose actions.
In his first comments about the U.S. nuclear arsenal since taking office on Jan. 20, Trump said he would like to see a world with no nuclear weapons but expressed concern that the United States has "fallen behind on nuclear weapon capacity."
"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," Trump said.
Russia has 7,300 warheads and the United States, 6,970, according to the Ploughshares Fund, an anti-nuclear group.
"The history of the Cold War shows us that no one comes out 'on the top of the pack' of an arms race and nuclear brinkmanship," said Daryl Kimball, executive director of the independent Arms Control Association non-profit group.