In addition, he noted that Gabbard, D-Hawaii, supported Sen. Bernie Sanders, I-Vt., in 2016.
"You have these people who, they've run for president...they lose, they're bitter, they're resentful," Zeldin told Hemmer. "The president won this office ... and, instead of working with this president and advocating for USMCA or reducing prescription drug prices and so much more, instead, there's that bitterness."
"You see it on the Democratic side with Hillary Clinton — and now she's going after Tulsi Gabbard calling her a 'Russian asset,'" he said.
Appearing on former President Obama aide David Plouffe's "Campaign HQ" podcast last week, Clinton accused Gabbard – although not referring to her by name – of being a "Russian asset" and a "third-party candidate."
“I'm not making any predictions but I think they've got their eye on somebody who is currently in the Democratic primary and are grooming her to be the third-party candidate,” Clinton said. “She's the favorite of the Russians. They have a bunch of sites and bots and other ways of supporting her so far.”
Gabbard lashed out at Clinton on Twitter Friday, calling her the "queen of warmongers [and the] embodiment of corruption" in response to the allegations.
She also told Fox News' Tucker Carlson on "Tucker Carlson Tonight" last week that Clinton is waging a smear campaign against her because "she knows she can't control me." She accused Clinton of having "blood on her hands" after the Iraq War she "championed."
"Their blood is on her hands. That's why she's smearing my character and trying to undermine my campaign," Gabbard said.
"I said, wait a minute, it took me two-and-a-half years, I wish she would have said that earlier because people... have realized she is crazy," he told Hannity. "She’s crazy.”
Some Democrats have made similar claims about Gabbard, but other prominent leaders have slammed Clinton.
"Tulsi Gabbard has put her life on the line to defend this country," wrote Sanders. "People can disagree on issues, but it is outrageous for anyone to suggest that Tulsi is a foreign asset."
"[Hillary is] not dealing with her loss well," said Zeldin. "She believes that ... the legacy of why she lost is due to – in her mind – the Russians changing the outcome of our election. I think she's convinced herself of it."
"She has this bitterness towards Russia because of it and she's gotten to the point where she also blames Tulsi Gabbard," he concluded.
Fox News' Matt London contributed to this report.