His decision removes the most likely barrier to the nomination of the only announced Republican contender thus far, Rep. Bill Cassidy (R-La.).

Fleming said in a statement that he decided against a run because he believes it could jeopardize GOP chances at toppling Sen. Mary LandrieuMary LandrieuCNN producer on new O'Keefe video: Voters are 'stupid,' Trump is 'crazy' CNN's Van Jones: O'Keefe Russia 'nothingburger' video 'a hoax' Trump posts O'Keefe videos on Instagram MORE (D-La.), considered by Republicans to be one of the most vulnerable Democrats in the nation.

"[The desire to replace Landrieu] is so strong, that for me to enter the race now would risk a contest between two experienced Republican Congressmen, potentially offering Senator Landrieu a path back to Washington. I can’t let that happen," he said in the statement, calling Cassidy "a Republican alternative necessary in 2014 to replace a big-government Washington liberal."

"Therefore, with prayerful analysis, my family and I have decided to step aside for this Senate race to optimize the chance for Republicans to win this vital seat," he adds.

Some Louisiana Republicans have expressed concern that, because of Louisiana's "jungle primary" system — wherein all candidates, regardless of party, are listed on the first ballot — multiple GOP candidates could hurt the party's chances at what they consider one of their top pickup opportunities in 2014.

President Obama lost Louisiana by more than 15 percentage points in 2012, and he and his policies — particularly ObamaCare — remain deeply unpopular in the state.

Cassidy announced his intentions to run Tuesday, and Fleming said shortly after that he hadn't ruled out a potential run, noting that Republicans need "a strong conservative candidate" in the race.

Though Cassidy has long been preparing for the race, and is considered a strong Republican recruit, he has a less conservative record than both Fleming and former Rep. Jeff Landry, who is also considering a run. That record was enough to keep the potential for a primary open.

Neither Landry nor another potential contender, Chas Roemer, son of former Gov. Buddy Roemer, has expressly ruled out challenging Cassidy. But with Fleming's decision not to enter the race, the threat of a primary diminishes.