This week The Guardian published an interview in which McIlroy -- the world's No. 1 player again -- said the game was not benefitting from the acrimony caused by the split between LIV and the PGA Tour.
Earlier this month Mickelson said he saw "LIV Golf trending upwards" and the "PGA Tour trending downwards," adding: "I love the side that I'm on." Yet, speaking ahead of the LIV finale at Trump National Doral in Miami, Mickelson appeared to regret those comments but praised LIV's rise.
"Maybe I shouldn't have said stuff like that, I don't know," Mickelson said.
"If I'm just looking at LIV Golf and where we are today to where we were six, seven months ago and people are saying this is dead in the water, and we're past that.
"Here we are today, a force in the game that's not going away."
McIlroy said the LIV series was "dead in the water" in February, around the time Dustin Johnson and Bryson DeChambeau said they would remain with the PGA Tour. They both left for LIV anyway, lured by signing bonuses reportedly worth in excess of $100 million. Johnson has earned about $31m more in LIV prize money heading into this weekend's finale.
McIlroy has made no secret about his feelings toward LIV and the players who decided to change tours.
"This 'us versus them' thing has gotten way out of control already," McIlroy told The Guardian. "If the two entities keep doubling down in both directions, it is only going to become irreparable. We are going to have a fractured sport for a long time. That is no good for anyone."
McIlroy returned to No. 1 in the world last weekend by winning the CJ Cup in South Carolina. Mickelson called it "a great win" and "an impressive victory."
"I think a lot of Rory," Mickelson said. "I really have the utmost respect for him, and I look at what he's done in the game and how he's played this year and his win last week and [how he is] No. 1 in the world now, and I have a ton of respect for him."
LIV Golf's finale is a team-only event that starts Friday and ends Sunday, with a $50m purse -- including $4m apiece to each member of the winning four-man team. The tour is funded by Saudi Arabia's sovereign wealth fund, and players who have been drawn to the large prizes have been banned from playing on the PGA Tour.
Lawsuits involving LIV players' participation in PGA Tour and European tour events are ongoing on both sides of the Atlantic. There is also uncertainty about who will be allowed to play in the Ryder Cup.
"I've always wanted to play Ryder Cups and have played with as much passion as anyone else that I've ever seen play a Ryder Cup," Ian Poulter, who has played for Europe in seven Ryder Cups and has been on the winning side five times, said.
That was in response to McIlroy telling The Guardian that he felt "betrayal" at how many of his past Ryder Cup teammates have gone to LIV in moves that "jeopardise" their future eligibility.
"I would like to think the Ryder Cup means as much to them as it does to me," McIlroy said. "Maybe it does. But knowing what the consequences could be, I just could never make that decision."