WASHINGTON — Former Gov. Terry McAuliffe of Virginia said Wednesday he would not run for president, concluding that his moderate profile would have limited appeal when Democratic voters appear to be choosing between younger, progressive contenders and veteran politicians like Senator Bernie Sanders and former Vice President Joseph R. Biden Jr., who is expected to enter the race next week.

“I would have loved to have run for president,” Mr. McAuliffe said in a telephone interview, but he conceded it would have been “a hard primary.”

A storied political fund-raiser and close friend of Bill and Hillary Clinton, Mr. McAuliffe had visited the early primary state of South Carolina and made calls to his donor network in hopes of lining up support. He said that he would have been able to raise $10 million in his first three months as a candidate. And with a record of job expansion during his tenure in Virginia, which he trumpeted at every opportunity, Mr. McAuliffe believed he could be a formidable candidate in a 2020 primary with no dominant front-runner.

But while the exuberant former Democratic National Committee chairman often sounded eager to run, and even tested a centrist message targeting what he called “dishonest populism,” it became clear to him that there was limited space for a 62-year-old political veteran.