Senate Majority Leader Mitch McConnell on Tuesday defended his plan to allow Republican senators currently in the leadership to run again for those positions in November.

Sen. Mike Lee, R-Utah, a relative newcomer to the Senate, is waging a bid to become Republican Policy Committee Chairman, a post now held by Sen. John Barrasso, R-Wyo. The effort has fueled a debate within the Senate Republican Conference over whether GOP elders should make way for new blood.

Lee is an ally of Senate firebrand and GOP presidential candidate Ted Cruz, who made a name for himself by bucking the leadership, particularly McConnell. Both men were elected to the Senate with the endorsement of the Tea Party.

McConnell said Barrasso can serve one more term in his leadership spot because his first year in office in 2011 filled a vacancy left when Sen. Lamar Alexander, R-Tenn., stepped down from leadership.

Lee, who took office in 2011, believes the half-term served by Barrasso should count as a full two-year term, thus excluding him from another term in leadership.

McConnell said he disagrees and won't exclude Barrasso, who plans to run again. He said the Senate has a precedent for the rule, including Sen. Don Nickles, who served as Republican whip from 1996 until 2003.

"It does not apply to a portion of the year," McConnell said of the term limits.

Republicans discussed the matter in a closed-door meeting on Tuesday. Sen. Jeff Sessions, R-Ala., who has endorsed Donald Trump for president, questioned additional terms for the current leadership lineup.

"This team has been together, they've worked hard and harmoniously," Sessions said. "But it's obvious a lot of people out in the country would like to see some changes in Washington. What's wrong with having some new people in the leadership? I think it would be healthy for the party and I would tend to favor that."

In addition to McConnell and Barrasso, the leadership is comprised of Majority Whip John Cornyn of R-Texas, Sen. John Thune of South Dakota, and Roy Blunt of Missouri, who serve as Republican Conference chair and vice chair, respectively.

Cornyn told the Washington Examiner the Republican leadership elections in November will give lawmakers the chance to elect new leaders if they choose.

"The best term limit is an election," Cornyn said.

Lee has the backing of FreedomWorks, a group associated with the Tea Party that backs conservative candidates. The group has at times been critical of the current leadership team and has sought a more conservative Senate agenda.

"We could not be more excited that Sen. Lee is seeking this post," FreedomWorks president CEO Adam Brandon said in a statement. "If he is elected, it would be a tremendous boost to grassroots conservative activists across the country and a sign that Senate Republicans are ready to pursue a bold policy agenda."