Sen. Mike Lee is calling on the candidates running to succeed Sen. Mitch McConnell as Republican leader to relinquish some of the power to rank-and-file GOP senators.

Mr. Lee, Utah Republican, sent a letter to his colleagues in which he argued that the cure to “unprecedented political tensions” is restoring the power voters have to enact change through their elected representatives.

“The best way we can help lower the temperature of our politics and restore public trust in our institutions is to ensure that the people have more say in the laws that govern their lives,” Mr. Lee wrote in the letter, which was obtained by The Washington Times. “We have a once-in-a-generation opportunity to do so with the upcoming election for our Senate Republican leadership.”

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The letter was reminiscent of the constraints House Republicans placed on Speaker Kevin McCarthy, who ultimately was kicked out of the job for not satisfying his right flank.

Three candidates are running to succeed Mr. McConnell, the longest-serving GOP leader in Senate history. Sens. John Thune of South Dakota and John Cornyn of Texas, respectively, the current and former GOP whip, are considered the favorites.

Mr. Lee often pushes back on decisions from Mr. McConnell and his deputies and is more politically aligned with dark-horse candidate Sen. Rick Scott of Florida. But he has not yet declared support for any of the three GOP leader candidates.

The GOP leadership election, which will determine who gets the top spot as well as lower-level leadership roles, is not yet scheduled but is expected to take place soon after the Senate returns in November.

In the letter, Mr. Lee said the current leadership-driven processes in the Senate have shut out individual senators and their constituents, leaving the American people feeling ignored.

He outlined three principles for “a better path forward” — equal representation, more time for debate and deliberation and strategically advancing Republican policies — along with some specific proposals for change.

One of Mr. Lee’s suggestions is to make it harder for the leader, when Republicans control the majority, to block senators from offering amendments to bills using a procedure known as filling the tree. He proposed a rule requiring three-fourths of the Republican Conference to agree before the procedure is used to cut off amendment debate.

“This would give individual members more say and restore the Senate as a place of genuine debate and negotiation,” Mr. Lee said. “Likewise, in circumstances where it is prudent to fill the tree, instead of bearing that burden alone, the Republican floor leader can do so with the support of the conference.”

Leaders fill the tree to control the fate of bills because otherwise, any senator from either party can go to the floor during debate and offer an amendment. That would make for a more open process but less certain vote outcome.

Mr. Lee frequently calls for the Senate to engage in more open debate, especially when it comes to the annual spending bills that are often negotiated by leadership and rushed through at the last minute to avoid a government shutdown.

In the letter, which was first reported by Politico, he proposes the GOP leader at the beginning of each year set a schedule for considering the 12 annual appropriations bills “to set the tone and pace of spending negotiations.”

And if final bicameral negotiations lead to an omnibus appropriations package combining all 12 bills, the GOP leader should ensure at least four weeks to debate and amend it, Mr. Lee said.

“Providing this time will allow us to craft better laws and give the American people a real opportunity to engage in the legislative process,” he said.

Mr. Lee also offered proposals to help Republicans ensure that the spending and other must-pass bills are not shaped primarily by Democrats.

The Republican leader should, at the start of each year, propose policy goals for the conference to ratify and then, throughout the year, present specific strategies for achieving GOP victories in connection with must-pass legislation, he said.

Mr. Lee would also like the leader and the GOP whip to formally push the conference to vote a certain way only when the majority of Republican senators agree.  

“This would protect Republican leadership from ever being in the position of having to whip for legislation advancing Democrat priorities, as happens from time to time when must-pass legislation is up against a critical deadline,” he said. “In such circumstances, Republican senators would be free to negotiate for their own priorities in order for that legislation to gain their support.”

Mr. Lee invited his colleagues to share their thoughts and suggestions on his proposals.

“I am confident that with the right leadership and a commitment to these reforms, we can create a stronger, more accountable Senate that truly serves the people,” he said.