Romney's decision will probably boost the fortunes of former Florida Governor Jeb Bush, a probable presidential candidate who, like Romney, is widely viewed as representing the Republican establishment.
Many who had raised money for Romney were already looking elsewhere, concerned that the former Massachusetts governor did not make sufficient changes from his 2012 campaign, when President Barack Obama defeated him.
"After putting considerable thought into making another run for president, I’ve decided it is best to give other leaders in the party the opportunity to become our next nominee," Romney said in a statement he read to supporters in a conference call from New York.
Romney told a private donors meeting in New York three weeks ago that he was considering jumping into the race. On Friday, he sounded reluctant to bow out.
The reaction to his potential candidacy was both surprising and heartening, he said, noting that he was leading in many national polls as well as in key swing states.
"So I am convinced that we could win the nomination, but fully realize it would have been difficult test and a hard fight," Romney said.
In his statement, Romney said he still believed he would have the best chance of beating the eventual Democratic nominee because of his message of "making the world safer" and improving the U.S. economy for the middle class.
But he said he did not want to make it more difficult for someone who might have a better chance of getting elected.
"I believe that one of our next generation of Republican leaders, one who may not be as well known as I am today, one who has not yet taken their message across the country, one who is just getting started, may well emerge as being better able to defeat the Democrat nominee," he said.
Bush said he recognized how hard the decision was for Romney. "Mitt is a patriot, and I join many in hoping his days of serving our nation and our party are not over," he said in a statement.
Romney, who also ran for the White House in 2008, would have faced difficulties raising money in a third run. Some of his fund-raisers said they were inclined to move on to other potential candidates like Bush.
Theresa Kostrzewa, a Raleigh, North Carolina, Republican who raised money for Romney in 2012, said she had wanted to hear him say he had learned from his mistakes in 2012 and would run a different campaign.
"What I think right now is his time has come and gone," she said. "I think he missed the boat."
In another troubling sign for Romney, David Kochel, a Republican strategist in Iowa who backed the candidate in past campaigns, was named on Thursday as a senior strategist for Bush.
Iowa Republican Renee Schulte, who had been a Romney supporter since 2006 and raised money for him in 2012, said she still thought he would be a great president if elected, but she did not see a path to victory.
"I've asked questions about what would be different, and I'm still waiting for answers," she said. "What's different?"