US President Donald Trump has reportedly told Russian President Vladimir Putin that if Washington and Moscow reignite the arms race, the United States would win.

NBC News quoted a Trump administration official on Thursday as saying:  "Putin's revelation of new nuclear-capable Russian weapons that can reach the United States really got under the president's skin".

"If you want to have an arms race we can do that, but I'll win," Trump reportedly told his Russian counterpart during a phone call last week.

Delivering his annual state of the nation speech in Moscow earlier this month, Putin expressed concerns about the new US nuclear posture which he said has lowered the threshold for the use of nuclear weapons.

Putin said:  "The new American policy allows the use of nuclear weapons in response to a conventional attack or even a cyber threat".  He added: "Russia reserves the right to use nuclear weapons only in response to a nuclear attack or an attack with other weapons of mass destruction against her or her allies, or a conventional attack against us that threatens the very existence of the state."

Putin also said that Russia had tested a number of new advanced strategic weapons, which could not be intercepted, saying they would render US-made defense missile systems "useless."  He also said that the West has ignored Russia but should “listen to us now.”

In last week’s phone call, Trump also congratulated Putin for his recent presidential election victory.

Following the phone call, Trump said that the two men had "a very good call" and that he was planning to meet with the Russian leader in the near future.