Network's contributor told "Fox and Friends" that Trump could "become kind of a generic name" for the vaccine.
Carlson said he asked Sidney Powell to produce evidence of her allegations but she was not forthcoming.
The Trump campaign has so far had little success with lawsuits aimed at challenging election results.
Tucker Carlson said that how one viewed Rudy Giuliani's Thursday press conference "depended largely on who you voted for."
"To have that accusation offhandedly thrown out there just to confuse our voters across the United States, I think that is absolutely wrong," she added.
White House Press Secretary Kayleigh McEnany said Wednesday that requiring poll watchers in Pennsylvania to stand "a football field away" during the vote-counting process was a "travesty."
The venerated newsman recently railed against media "enablers" for the spread of misinformation about COVID-19.
Brian Kilmeade's remarks join those of several Republicans asking President Donald Trump to acknowledge the election results and move forward with the transition of power.
While appearing on Fox News' Fox & Friends on Wednesday, Kayleigh McEnany was asked what she thinks of the different suggestions and guidelines medical professionals have released in an effort to mitigate the spread of the coronavirus during Thanksgiving.
Fox News anchor said that the PAC was engaged in a "crackdown" on law firms representing the president's case.
CNN alleged that the pile of paperwork presented on television by White House Press Secretary Kayleigh McEnany was "full of nothing."
Hannity insisted that the 73 million Americans that voted for Trump won't "just go away."
"DEAD PEOPLE VOTED," the president tweeted.
A former competitor of the reality cooking showed died tragically at the young age of
Trump attorney Sidney Powell uttered the phrase recently, and social media went wild with it.
"Over the weekend we got a lot of calls asking if this show was leaving Fox News," Tucker Carlson said during his Monday broadcast.
A closer look at the frequent guest host (and possible successor) of the popular conservative radio show.
"We just saw a very disturbing sign, it said 'Coming for Blacks and Indians first, welcome to the New World Order,'" Fox News anchor Eric Shawn said.
Some Trump supporters have turned their backs on Fox News since the network called the state of Arizona for President-elect Joe Biden.
The president also said that his supporters at the event wouldn't "stand for a Rigged and Corrupt Election."
"I don't know even know if I agree with it, but that happens sometimes," Pete Hegseth told viewers.
On November 11, the Trump campaign falsely claimed that James Blalock had passed away 14 years ago but illegally voted this year. Tucker Carlson later amplified the claim on his show.
Fox News anchor Chris Wallace said that President Donald Trump's claims of election manipulation would have to prove "fraud of a dimension that it would actually overturn the results."
Fox News has gained the ire of the right-wing after declaring Biden as the winner of Arizona during Election Night and for declaring him as the winner of the election.
Al Schmidt, one of Philadelphia's GOP city commissioners, refuted President Trump's claims about voter fraud.
Fox News has been a staple for many on the right and has had constant support from President Donald Trump since he has been in office. Is that beginning to change?
Control of the Senate will be decided in Georgia on January 5 in what is expected to be an expensive race.
Experts have dismissed allegations that dead people cast ballots, saying the rumour comes up every election.
The top public health expert was subject to several allegations from Ingraham and White House adviser Scott Atlas on Tuesday night.
In response to Trump's tweets being flagged as misleading, Hannity asked if everybody could move to "free speech social network" Parler.