The United States does not see an increased risk of Russia using nuclear weapons over its war in Ukraine even as Moscow has recently been escalating its rhetoric, a senior U.S. defense official said Friday.

"We continue to monitor their nuclear capabilities every day the best we can. And we do not assess that there is a threat of the use of nuclear weapons and no threat to NATO territory," the official said.

Russian President Vladimir Putin warned on Wednesday of the possibility of "lightning-fast" retaliatory strikes if a third country intervenes in military operations in Ukraine and poses threats to Russia. He said Russia possesses weapons others do not have and that his country will "use them if needed."

On Monday, Russian Foreign Minister Sergey Lavrov said the danger of a nuclear war is "serious" and "real," and that "it should not be underestimated."

Russia began its invasion of Ukraine in late February, after having asserted that its own security has been under threat with NATO's eastward expansion and the possibility of Ukraine's membership in the alliance.

But its military campaign has apparently not gone as initially planned, with Russian forces failing to seize Ukraine's capital in the face of fierce resistance from the East European country.

The U.S. administration of President Joe Biden has maintained it will not send American troops to Ukraine amid concerns that being drawn into a direct conflict with nuclear-armed Russia would result in "World War III."

But the United States, along with other NATO member countries, has provided security assistance to Kyiv to help it defend itself against Russia's invasion.