After his 2012 loss to President Barack Obama, Romney enjoyed a surge of popularity in his party as some trumpeted his international prognostications—especially that Russia posed a greater threat to global stability than his opponent allowed at the time.
In his prepared remarks to supporters Romney said he thought that a third attempt at the presidency would have been competitive.
"I am convinced that with the help of the people on this call, we could win the nomination. Our finance calls made it clear that we would have enough funding to be more than competitive," the remarks said. "With few exceptions, our field political leadership is ready and enthusiastic about a new race. And the reaction of Republican voters across the country was both surprising and heartening."
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"So I am convinced that we could win the nomination, but fully realize it would have been [a] difficult test and a hard fight," Romney's remarks said.
After Friday's announcement, former Florida Gov. Jeb Bush, a potential 2016 presidential candidate, praised Romney.
"Mitt Romney has been a leader in our party for many years," Bush said in a statement. "There are few people who have worked harder to elect Republicans across the country than he has. ... Mitt is a patriot and I join many in hoping his days of serving our nation and our party are not over. I look forward to working with him to ensure all Americans have a chance to rise up."
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Florida Sen. Marco Rubio said in a statement that "[o]ver the past two years, there hasn't been a day when I didn't think that Mitt Romney would have been a better president than Barack Obama." Rubio added that he "deeply" respects Romney's "decision to give the next generation a chance to lead."
A statement from Kentucky Sen. Rand Paul said he hopes to work with Romney "to grow our party and lead our country forward."
—Reuters contributed to this report.