Russian politicians have warned that US President Donald Trump's declared plan to put the US nuclear arsenal in a higher position compared to other countries runs the risk of triggering a new arms race between Washington and Moscow.

"Trump's campaign slogan 'Make America great again', if that means nuclear supremacy, will return the world to the worst times of the arms race in the '50s and '60s," Konstantin Kosachev, the chairman of the international affairs committee in the upper house of the Russian parliament, wrote in a message on social media on Friday.

Kosachev said the Cold War era arms race during the '50s and '60s had been a dangerously grave time in human history that ended peacefully after the abandonment of the idea of nuclear supremacy.

"Over the course of the Cold War, the Soviet Union and the United States realized that achieving supremacy was dangerous, and accepted the doctrine of parity as the best way to ensure peace," he wrote.

Alexei Pushkov, a member of the defense and security committee in Russia's upper house of parliament, also commented on the matter in a message on social media.

"The United States cannot achieve decisive [nuclear] superiority … Instead of trying to achieve an illusory nuclear supremacy over Russia, the US administration should find a solution to the exceptionally complicated nuclear problem of North Korea."

This file photo taken on November 1, 1952 from Majuro Atol shows the explosion of the US's first H-bomb at Enewetak Atoll, in the Marshall Islands.(Photo by AFP)

Pushkov and Kosachev are not directly involved in decision-making on the Russian foreign policy and defense strategy. However, they both reflect the Kremlin’s position on state matters.

In a Thursday interview with Reuters, Trump had said he wanted to expand America’s nuclear arsenal to ensure it was at the "top of the pack," saying the United States had fallen behind in its nuclear weapons capacity.