Asked in a CNN interview last week about his party’s turn to the left, Mr. Clinton contended that he “ran on income inequality in 1992.” Without prompting, he brought up Ms. Warren as he defended his administration’s approach to bank regulation. In 1999, Mr. Clinton signed legislation that repealed parts of the Glass-Steagall Act, allowing the commingling of commercial and investment banking, a move much criticized by the left since the financial crisis of 2008.

“When they pass bills with a veto-proof majority, with a lot of Democrats voting for it, that I couldn’t stop, all of a sudden we turn out to be maniacal deregulators,” Mr. Clinton said, lamenting the liberal perception of his financial policies. “I mean, come on. I know that Senator Warren said the other day, admitted, when she introduced a bill to reinstate the division between commercial and investment banks, she admitted that the repeal of Glass-Steagall did not cause one single solitary financial institution to fail.”

Privately, some Democratic donors from the financial industry seem unnerved by Ms. Warren’s rise, underscoring the tension between the party’s liberal and centrist wings.

“People on Wall Street perceive her to be hostile to their industry, and so there was pretty widespread terror when she got on the Banking Committee,” said Steven Rattner, a New York financier and pillar of Mrs. Clinton’s fund-raising network.

The ascendant power of Ms. Warren and her fellow populists is best captured by their torpedoing this month of Lawrence H. Summers, Mr. Clinton’s treasury secretary, who was blocked before President Obama could even nominate him to lead the Federal Reserve. And the victory of Bill de Blasio, who hammered home a message of income inequality, in New York City’s Democratic primary for mayor has given the party’s progressive base even more confidence.

In the interview, Ms. Warren, 64, said twice that she had no interest in running for president, a point her aides amplify privately. But she said she would continue to focus on economic fairness, saying it is the signal issue of the day.

“This is the work America needs to take on, the work of making certain we strengthen the middle class,” Ms. Warren said. “This country should not be run for the biggest corporations and largest financial institutions.”