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.
Trump also expressed support for the European Union as a governing body, saying "I'm totally in favor of it," and for the first time as president expressed a preference for a two-state solution to the Israeli-Palestinian conflict, but said he would be satisfied with whatever makes the two sides happy.
Trump also predicted his efforts to pressure NATO allies to pay more for their own defense and ease the burden on the U.S. budget would reap dividends. "They owe a lot of money," he said.
Read alsoTrump outraged by Russian deployment of cruise missiles, vows to raise issue with PutinIn his first comments about the U.S. nuclear arsenal since taking office on Jan. 20, Trump was asked about a December tweet in which he said the United States must greatly strengthen and expand its nuclear capacity "until such time as the world comes to its senses regarding nukes."
Trump said in the interview 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 ... 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 7,000 warheads and the United States, 6,800, according to the Ploughshares Fund, an anti-nuclear group.
"Russia and the United States have far more weapons than is necessary to deter nuclear attack by the other or by another nuclear-armed country," said Daryl Kimball, executive director of the independent Arms Control Association non-profit group.
The new strategic arms limitation treaty, known as New START, between the United States and Russia requires that by February 5, 2018, both countries must limit their arsenals of strategic nuclear weapons to equal levels for 10 years.
The treaty 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, and contains equal limits on other nuclear weapons.
Analysts have questioned whether Trump wants to abrogate New START or would begin deploying other warheads.
In the interview, Trump called New START "a one-sided deal."
"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," he said.