Forgoing any appeals for healing or reflection, right-wing media organizations that spread former President Donald J. Trump’s distortions about the 2020 election continued on Wednesday to push conspiracy theories about large-scale fraud, with some predicting more political conflict in the months ahead.

The coverage struck a discordant tone, with pro-Trump media and President Biden in a jarring split screen: There was the new president delivering an inaugural address of unity and hope, while his political opponents used their powerful media platforms to rally a resistance against him based on falsehoods and fabrications.

For some outlets, like One America News, it was as if Mr. Biden weren’t president at all. The network, a favorite of Mr. Trump’s because of its sycophantic coverage, didn’t show its viewers Mr. Biden’s swearing in or his inaugural address.

Rush Limbaugh, broadcasting his weekday radio show a few miles from the Palm Beach retreat where Mr. Trump is spending the first days of his post-presidency, told his millions of listeners on Wednesday that the inauguration of Mr. Biden and Vice President Kamala Harris did not make them the rightful winners of the election.

“They have not legitimately won yet,” Mr. Limbaugh said, noting that he would be on “thin ice” for making such a claim. He then gave his listeners a false and inflated vote total for Mr. Trump and predicted the Democratic victories would be “fleeting.”

“I think they know, with 74 million, maybe 80 million people who didn’t vote for Joe Biden, there is no way they can honestly say to themselves that they represent the power base in the country,” Mr. Limbaugh said.

On One America News, viewers saw a lengthy documentary-style segment called “Trump: Legacy of a Patriot” instead of the inauguration. One of the network’s commentators, Pearson Sharp, provided the voice-over and offered only flattering words about the former president while he leveled false claims about voter fraud.

Mr. Sharp repeated many of the discredited excuses that have formed the alternate version of events that Mr. Trump and his followers are using to explain his loss. The host claimed, for instance, that Mr. Trump couldn’t have been defeated because he won the bellwether state of Ohio and carried so many more counties than Mr. Biden did. “And yet somehow we’re still expected to believe that Joe Biden got more votes than any president in history,” Mr. Sharp said.

Then he issued a rallying cry to Trump supporters. “Now it’s up to the American people to continue President Trump’s fight, or all the progress we’ve made as a nation will quickly unravel,” Mr. Sharp said.

OAN personalities were also offering viewers an optimistic vision of a Republican Party that would live on in Mr. Trump’s image. The network’s White House correspondent, Chanel Rion, described Mr. Trump’s farewell remarks from Joint Base Andrews on Wednesday morning as “a temporary goodbye.”

“The fight has only just begun,” she said.

One OAN anchor discussed the possibility that Mr. Trump could form his own political party and call it the Patriot Party, an idea that other Trump allies have started floating. And there was talk on the network of Ivanka Trump, the former president’s daughter, challenging Senator Marco Rubio, a Florida Republican, when he is up for re-election in 2022.

On Newsmax TV, another pro-Trump channel, commentators and guests appeared to be in less denial than their competitors on OAN. But they were no less dismissive of the new president. One questioned Mr. Biden’s appointment of a transgender woman to his cabinet and called the heavy presence of troops in Washington to prevent another uprising of Trump supporters an effort “to further suppress the voice of the American people.”

A Newsmax anchor mockingly pointed out the presence of Mr. Biden’s son Hunter, whose personal troubles and business interests became a distraction for his father’s campaign after conservative media outlets published unverified stories about his work in China. “That doesn’t go away,” the anchor said.