The use of language seen as containing coded racism prompted an extraordinary rebuke from the network.
"We do not condone this language and wanted to make our viewers aware that he has since clarified his statement," Fox News Channel's Sandra Smith said on air. Smith also read from a statement in which DeSantis' campaign suggested it was "absurd" to characterise the candidate's remarks as racist.
The NAACP Florida State Conference responded to DeSantis, calling comparisons to monkeys "by far the best-known racist references to African Americans in our national folklore."
In an interview on the network, Gillum suggested that DeSantis was "taking a page directly from the campaign manual of Donald Trump."
He added: "In the handbook of Donald Trump they no longer do whistle calls - they're now using full bullhorns," Gillum said.
Asked about DeSantis' comments by reporters at the White House, Trump said he "didn't hear" the Florida Republican's remarks, but he continued to praise him.
"He's an extreme talent," Trump said of DeSantis.
Earlier, Trump had attacked Gillum in a tweet, calling him a "failed Socialist Mayor" and the "biggest dream" for DeSantis, whose victory over a more moderate opponent in yesterday's GOP primary was propelled by Trump's endorsement.
Trump alleged that Gillum "has allowed crime & many other problems to flourish in his city," adding: "This is not what Florida wants or needs!"
Gillum fired back at the President on Twitter, writing: "What our state and country needs is decency, hope, and leadership."
With his primary win, Gillum became the first African-American nominee for governor of the country's third-most-populous state, emerging as a new focal point for the national party's liberal wing. He has embraced liberal policies, such as a "Medicare-for-all" health-care system, but he has not identified as a socialist.
The Florida race now stands as a national test for the base of each major party - as well as of Trump's swaying power.
Gillum said in a CNN interview that he does not fear Trump's expected heavy involvement in the general election - and that he "absolutely" believes the President should be impeached.
"Donald Trump and Ron DeSantis are both scraping from the bottom of the barrel," Gillum said. "I actually believe that Florida and its rich diversity are going to be looking for a governor that's going to bring us together, not divide us, not misogynists, not racists, not bigots."
DeSantis' "monkey this up" comments brought a swift condemnation from Terrie Rizzo, chairwoman of the Florida Democratic Party. The Democratic Governors Association and other political groups also levied criticism.
"It's disgusting that Ron DeSantis is launching his general election campaign with racist dog whistles," Rizzo wrote on Twitter.
Stephen Lawson, a DeSantis spokesman, later said that any characterisations of racism were unwarranted.
"Ron DeSantis was obviously talking about Florida not making the wrong decision to embrace the socialist policies that Andrew Gillum espouses," Lawson said. "To characterize it as anything else is absurd."
Former Republican National Committee chairman Michael Steele on MSNBC described DeSantis's remarks as "how white folks talk about black men who are successful."
Gillum yesterday presented himself as an unusual Democrat with the ability to bring together various factions of his party because he had received support from Senator Bernie Sanders, (I), even after he had backed Hillary Clinton in the 2016 presidential race.
Asked in a Washington Post interview about the chance to be Florida's first black governor, Gillum said, "I'm trying to be the next governor of Florida. I just happen to be black."
But he also has argued that his "lived experience" growing up in a working-class family in which he was the first to attend college has helped him connect with struggling Florida voters.
Gillum has also drawn parallels between his candidacy and that of Georgia's Stacey Abrams, the first black woman in the country to win a major-party governor nomination.
"The same part of this country that was built by people of colour may soon be led by people of colour," he said.
