Mr Trump made the statement in a tweet
President-elect Donald Trump wants the United States to "greatly strengthen and expand" its nuclear capability.
In a tweet, he appeared to suggest he wants America to continue in its perceived role as the world's police force.
He tweeted: "Must greatly strengthen and expand its nuclear capability until such time as the world comes to its senses regarding nukes.
The United States must greatly strengthen and expand its nuclear capability until such time as the world comes to its senses regarding nukes— Donald J. Trump (@realDonaldTrump) December 22, 2016
His comments come a day after he met top military officials to discuss defence budgets.
They included Lieutenant General Jack Weinstein, the deputy chief of staff for strategic deterrence and nuclear integration for the US air force.
During the presidential campaign, defeated Democratic candidate Hillary Clinton repeatedly claimed the Republican was too erratic and unpredictable to have control of the country's nuclear arsenal.
Ten former nuclear missile launch operators also wrote that Mr Trump lacked the temperament, judgement and diplomatic skill to avoid nuclear war.
In March, Mr Trump had suggested the world would be "better off" if other countries, including Japan and South Korea, had nuclear capabilities.
He said: "It's going to happen, anyway. It's only a question of time. They're going to start having them, or we have to get rid of them entirely."
The Republican candidate also said he "hated" nuclear proliferation "more than any".
Mr Trump was then asked by an interviewer: "So, you're saying you don't want more nuclear weapons in the world, but you're okay with Japan and South Korea having nuclear weapons?"
The tycoon responded: "I don't want more nuclear weapons", adding: "We can't afford it anymore."