US Central Intelligence Agency Director (CIA) Director William Burns. AP
The White House National Security Council said the CIA chief was to deliver a message to Sergei Naryshkin, head of Russia's SVR foreign intelligence service, "on the consequences of the use of nuclear weapons by Russia, and the risks of escalation to strategic stability."
It said Burns was not meeting with Naryshkin to negotiate anything, as the Ukraine war is in its ninth month and Russia still occupies large swathes of Ukraine territory.
"He is not conducting negotiations of any kind. He is not discussing settlement of the war in Ukraine," the NSC said in a statement.
"We firmly stick to our fundamental principle: nothing about Ukraine without Ukraine," it said.
The United States has warned for months against Russia's suggestions that it would use tactical nuclear weapons in Ukraine if its own territorial integrity was threatened.
Burns was also to raise with the SVR chief the issue of US citizens detained "unjustly" in Russia.
Russia has imprisoned US basketball star Brittney Griner on drug charges as well as Paul Whelan, an auto supply company official who was arrested in 2018 and convicted of spying.
Washington has reportedly offered a prisoner swap, with speculation that it is willing to exchange jailed Russian arms dealer Viktor Bout for the Americans.
Last week US President Joe Biden voiced hope that his Russian counterpart Vladimir Putin would negotiate "more seriously" to free Griner, who was sent to a penal colony on a nine-year sentence after her appeal in Russian courts failed.
"My hope is that now that the election is over that Mr. Putin will be able to discuss with us and be willing to talk more seriously about prisoner exchange," Biden said.