Mr. Sanders’s criticism of the Center for American Progress, delivered on Saturday in a letter obtained by The New York Times, reflects a simmering ideological battle within the Democratic Party and threatens to reopen wounds from the 2016 primary between him and Hillary Clinton’s allies. The letter airs criticisms shared among his supporters: That the think tank, which has close ties to Mrs. Clinton and the Democratic Party establishment, is beholden to corporate donors and has worked to quash a leftward shift in the party led partly by Mr. Sanders.

“This counterproductive negative campaigning needs to stop,” Mr. Sanders wrote to the boards of the Center for American Progress and its sister group, the Center for American Progress Action Fund. “The Democratic primary must be a campaign of ideas, not of bad-faith smears. Please help play a constructive role in the effort to defeat Donald Trump.”

Mr. Sanders sent the letter days after a website run by the action fund, ThinkProgress, suggested that his attacks on income inequality were hypocritical in light of his growing personal wealth.