After President Vladimir V. Putin of Russia claimed that action against Ukraine was taken in self-defense, the Fox News host Tucker Carlson and the conservative commentator Candace Owens repeated the assertion. When Mr. Putin insisted he was trying to “denazify” Ukraine, Joe Oltmann, a far-right podcaster, and Lara Logan, another right-wing commentator, mirrored the idea.

The echoing went the other way, too. Some far-right American news sites, like Infowars, stoked a longtime, unfounded Russian claim that the United States funded biological weapons labs in Ukraine. Russian officials seized on the chatter, with the Kremlin contending it had documentation of bioweapons programs that justified its “special military operation” in Ukraine.

As war has raged, the Kremlin’s talking points and some right-wing discourse in the United States — fueled by those on the far right — have coalesced. On social media, podcasts and television, falsehoods about the invasion of Ukraine have flowed both ways, with Americans amplifying lies from Russians and the Kremlin spreading fabrications that festered in American forums online.

By reinforcing and feeding each other’s messaging, some right-wing Americans have given credibility to Russia’s assertions and vice versa. Together, they have created an alternate reality, recasting the Western bloc of allies as provokers, blunderers and liars, which has bolstered Mr. Putin.

The war initially threw some conservatives — who had insisted no invasion would happen — for a loop. Many criticized Mr. Putin and Russia’s assault on Ukraine. Some have since gone on to urge more support for Ukraine.

But in recent days, several far-right commentators have again gravitated to narratives favorable to Mr. Putin’s cause. The main one has been the bioweapons conspiracy theory, which has provided a way to talk about the war while focusing criticism on President Biden and the U.S. government instead of Mr. Putin and the Kremlin.

“People are asking if the far right in the U.S. is influencing Russia or if Russia is influencing the far right, but the truth is they are influencing each other,” said Thomas Rid, a professor at Johns Hopkins University who studies Russian information warfare. “They are pushing the same narratives.”

Their intersecting comments could have far-reaching implications, potentially exacerbating polarization in the United States and influencing the midterm elections in November. They could also create a wedge among the right, with those who are pro-Russia at odds with the Republicans who have become vocal champions for the United States to ramp up its military response in Ukraine.

“The question is how much the far-right figures are going to impact the broader media discussion, or push their party,” said Bret Schafer, a senior fellow for the Alliance for Securing Democracy, a Washington nonprofit. “It serves them, and Russia, to muddy the waters and confuse Americans.”

Many of their misleading war narratives, which are sometimes indirect and contradictory, have reached millions. While Facebook, YouTube, Twitter and other platforms limited the reach of Russian state media online after the war began, a variety of far-right Telegram channels, blogs and podcasts took up the task of spreading the Kremlin’s claims. Inside Russia, state media has in turn reflected what some far-right Americans have said.

Mentions of bioweapons labs related to war in Ukraine, for example, have more than doubled — to more than 1,000 a day — since early March on both Russian- and English-language social media, cable TV, and print and online outlets, according to the media tracking company Zignal Labs.

The unsubstantiated idea began trending in English-language media late last month, according to Zignal’s analysis. Interest faded by early March as images of injured Ukrainians and bombed cities spread across the internet.

But Russia breathed new life into the conspiracy theory on March 6 when its Defense Ministry claimed in a televised address that it had uncovered “traces of a military biological program being implemented in Ukraine, funded by the U.S. Department of Defense.”

Mr. Carlson later aired the Russian statement on his show. Fox News declined to comment and pointed to segments where Mr. Carlson has criticized Mr. Putin.

Russia laid much of the groundwork for its convergence with many on the American right years ago. Before the 2016 U.S. presidential election, the Kremlin-backed Internet Research Agency, an organization that professionalized online disinformation, spread inflammatory content through Facebook and other social platforms to sow divisions among Americans and boost Donald J. Trump, the Republican nominee.

After Mr. Trump was elected, he publicly complimented Mr. Putin, once calling him “a genius.” The comments helped seed a favorable view of Mr. Putin’s strongman style of governance among some Americans.

The coronavirus pandemic further aligned some on the far right with Russia’s propaganda machine. Both sought to undercut confidence in vaccines and mask mandates to foment distrust in the federal government and health agencies. Anti-vaccine Facebook groups and Telegram channels became fertile ground for members of the far right and Russian trolls to hunt for conspiracy theories to promote, Mr. Schafer said.

Last month, the coalescing crystallized. As Western intelligence showed that Russia was preparing to invade Ukraine, Mr. Putin declared Ukraine an American colony with a “puppet regime” and denied that he planned an invasion.

In the United States, Mr. Carlson also called Ukraine “an obedient puppet of the Biden State Department.”

On Feb. 16, Russian state-owned media claimed that Ukraine had “fired mortar shells” at a separatist enclave within Ukraine backed by Russia. Charlie Kirk, a conservative activist, quoted the Russian media’s false assertion on his Telegram channel to 256,000 subscribers. Days later, Mr. Kirk also described the heightened situation as a “border dispute.”

A spokesman for Mr. Kirk said it was “patently false” that the podcaster was sympathetic to Russia’s invasion and that he was “rightly questioning” U.S. foreign policy.

On Feb. 24, Mr. Putin delivered a speech justifying an invasion of Ukraine. It was transcribed in full on Infowars. On Twitter, Ms. Owens, the conservative commentator, repeated Mr. Putin’s claim that NATO was expanding eastward toward Russia, blaming the United States for the war. She urged her three million followers to read Mr. Putin’s speech directly to learn what was “actually” going on.

In an email, Ms. Owens said she encouraged “all citizens to read speeches that are given by leaders around the world to better understand their motivations behind actions.” Infowars did not respond to requests for comment.

But the invasion proved highly unpopular among many Americans, leading to a backlash against those who seemed to side with Mr. Putin. After the far-right podcaster Mr. Oltmann said on his Feb. 24 show that he would “stand on the side of Russia,” his co-host, Max McGuire, pushed back.

“Russia’s the bad guy in this situation,” Mr. McGuire said. Mr. Oltmann and Mr. McGuire did not respond to requests for comment.

Others on the right refuted some Kremlin talking points, including that neo-Nazis are rampant in Ukraine and that President Volodymyr Zelensky is a “drug-addled Nazi.” On Feb. 26, the Fox News host Neil Cavuto said those accusations were “incredibly over-the-top crazy criticisms.” (Mr. Zelensky, who is Jewish, signed a law combating antisemitism last fall.)

The lull did not last. American anti-vaccine channels on Telegram soon picked up the bioweapons conspiracy theory, which jumped from private chat groups to far-right podcasts and Infowars.

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.”