When Victoria Nuland, an under secretary of state, was questioned in the Senate this month over whether Ukraine had biological weapons, she said laboratories in the country had materials that could be dangerous if they fell into Russian hands. Jack Posobiec, a far-right commentator, insinuated on his March 9 podcast that Ms. Nuland’s answer bolstered the conspiracy theory.

“Everybody needs to come clean about what was going on in those labs, because I guarantee you the Russians are about to put all of it onto the world stage,” said Mr. Posobiec, who did not respond to calls seeking comment.

Russian officials also latched on to Ms. Nuland’s comments. “The nervous reaction confirms that Russia’s allegations are grounded,” the country’s official account for the Ministry of Foreign Affairs posted on Twitter.

Beyond the bioweapons conspiracy theory, Joseph Jordan, a white nationalist podcaster who goes by the pseudonym Eric Striker, repeated Russia’s claim that a pregnant woman who was injured in the bombing of a Ukrainian maternity hospital had faked her injuries. In his Telegram channel, Mr. Jordan told his 15,000 followers that the hospital photos had been “staged.” He did not respond to a request for comment.

Some Russians have publicly commented on what appears to be common ground with far-right Americans. Last week on the Russian state-backed news program “60 Minutes,” which is not connected to the CBS show of the same name, the host, Olga Skabeeva, addressed the country’s strengthening ties with Mr. Carlson.

“Our acquaintance, the host of Fox News Tucker Carlson, obviously has his own interests⁠,” she said, airing several clips of Mr. Carlson’s show where he suggested the United States had pushed for conflict in Ukraine. “But lately, more and more often, they’re in tune with our own.”