Escalating the war of words between Wall Street and Senator Elizabeth Warren, Leon Cooperman, a billionaire money manager, denounced her recent tweet encouraging him to “pitch in a bit more” because of his success in life, saying she sounded like “a parent chiding an ungrateful child.”

“However much it resonates with your base, your vilification of the rich is misguided,” wrote Mr. Cooperman, the billionaire manager of the Omega Family Office, in an Oct. 30 letter made public on Thursday. “For you to suggest that capitalism is a dirty word and that these people, as a group, are ingrates who didn’t earn their riches … and now don’t pull their weight societally indicates that you either are grossly uninformed or are knowingly warping the facts.”

Mr. Cooperman’s letter was the culmination of weeks of long-distance tension with Ms. Warren, the Massachusetts Democrat who has styled herself as a capitalist who nevertheless wants to overhaul the excesses of Wall Street and raise taxes on the country’s richest. Like many money managers and investors, Mr. Cooperman, the 76-year-old former hedge fund manager, has taken umbrage at Ms. Warren’s critique of the finance industry and like others on Wall Street predicts there will be stock-market losses if she were to win the presidency.

Ms. Warren’s campaign did not immediately respond to a request for comment to Mr. Cooperman’s remarks, which were first published by CNBC.com on Thursday afternoon before going viral. But later, she wrote on Twitter: “Leon is wrong. I’m fighting for big changes like universal child care, investing in public schools, and free public college. We can do all of that with a #TwoCentWealth Tax. Leon can and should pitch in more—so that every kid has the same opportunities he did to succeed.”