(CNN) Retiring Republican Sen. Jeff Flake said Wednesday that he will not vote to confirm the Trump administration's judicial nominees on the Senate floor or advance them in the Senate Judiciary Committee if legislation to protect special counsel Robert Mueller does not receive a Senate floor vote.

Flake made the new judicial threat after he and Sen. Chris Coons, a Delaware Democrat, unsuccessfully attempted to force a Senate vote on the special counsel legislation Wednesday. Senate Majority Leader Mitch McConnell objected to the request for a vote from Flake.

But the Arizona Republican's threats on judicial nominees could complicate matters in the Judiciary Committee, where Republicans have an 11-10 majority. There are currently 21 judicial nominees pending in the committee and 32 who are awaiting a floor vote, Flake said.

"We have been told that the bill that Sen. Coons and I will move to bring up shortly is not necessary, as there have been no indications that the independence of Mr. Mueller's investigation is in jeopardy," Flake said. "That may have been an arguable position before last week. But it is not arguable anymore."

Flake and a handful of other Republican senators, such as Susan Collins of Maine, have said they think the legislation to protect the special counsel is necessary after President Donald Trump fired his attorney general, Jeff Sessions, and replaced him with acting Attorney General Matt Whitaker, who has been openly critical of the Mueller probe.

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