Mr Trump had earlier called for an expansion of US nuclear capabilities in a tweet that alarmed non-proliferation experts who said that boosting the US arsenal could fuel global tensions.
In his Twitter post, Mr Trump said: “The United States must greatly strengthen and expand its nuclear capability until such time as the world comes to its senses regarding nukes.”
But the President-elect gave no further details.
It was not clear what prompted his comment but earlier in the day Vladimir Putin said that Russia needed to “strengthen the military potential of strategic nuclear forces.”
Trump spokesman Sean Spicer has attempted to play down the threat insisting there will be no arms race because the President-elect would make sure countries trying to step up their nuclear capabilities, such as Russia and China, would back down.
Mr Spicer said: “He’s going to ensure that other countries get the message that he’s not going to sit back and allow that.
“And what’s going to happen is they will come to their senses, and we will all be just fine.”
But the 70-year-old told US breakfast show Morning Joe he would accept an arms race.
Mr Trump’s comments have been met with astonishment in the US.
Daryl Kimball, executive director of the Arms Control Association, a leading proponent of arms control based in Washington, said: “It is completely irresponsible for the president-elect or the president to make changes to U.S. nuclear policy in 140 characters and without understanding the implications of statements like ‘expand the capacity.
“He must have leaders around the world trying to guess what he means. This is Bush league.”
Joe Cirincione, president of Ploughshares Fund, a foundation that works to prevent the spread and use of nuclear weapons, said: “This is how arms races begin – with a battle of words.
“Neither side needs to be spending hundreds of billions of dollars on nuclear weapons we don’t need.”