"What we need to be looking at is whether this election was rigged by Donald Trump and his buddy Vladimir Putin," Perez said in an interview with CNN's Jake Tapper on "State of the Union" on Sunday.
Perez argued that Attorney General Jeff Sessions can't adequately investigate any possible connections because the Alabama Republican was a close adviser and supporter of Trump during his presidential campaign.
"It's really unfair to any foxes around the country to say that would be the fox guarding the hen house," Perez said.
Asked about the issue Sunday on ABC's "This Week," White House spokeswoman Sarah Huckabee Sanders said it's too early to call on Sessions to recuse himself from the investigation.
"I wasn't saying that he shouldn't recuse himself or that he should," Sanders said. "My point is, I don't think we're there yet. Let's work through this process. You guys want to jump to the very end of the line. That's not how this works. Typically, you go through a congressional oversight review. We're doing that. Let's not go to the very end of the extreme. Let's let this play out the way it should."
Trump tweeted on Sunday afternoon about the Russia-related news coverage, calling it "fake news" that's being stirred up for political reasons.
Perez's comments on "State of the Union" came after Tapper asked him about Trump's accusation in a Sunday morning tweet that he won the race for DNC chairman Saturday over Minnesota Rep. Keith Ellison, who was backed by Bernie Sanders and the party's progressive wing, because the process was "rigged."
Trump tweeted: "The race for DNC Chairman was, of course, totally 'rigged.' Bernie's guy, like Bernie himself, never had a chance. Clinton demanded Perez!"
Perez appointed his rival for the top DNC spot, Minnesota Rep. Keith Ellison as his deputy after winning Saturday and laughed off Trump's assertion that his 235-vote to 200-vote win was because of a rigged system.
"Our unity as a party is our greatest strength, and it's his worst nightmare," Perez said of Trump.