The president-elect, who takes office next month, said the US must take such action “until such time as the world comes to its senses regarding nukes”.
His spokesman later said that he was referring to the need to prevent nuclear proliferation.
Mr Trump spoke hours after President Vladimir Putin said Russia needs to bolster its military nuclear potential.
The US has 7,100 nuclear weapons and Russia has 7,300, according to the US nonpartisan Arms Control Association.
Mr Trump’s comments came in the form of a tweet, giving no other details.