PORTLAND, Maine—Sen. Bernie Sanders and his top aides showed no sign they would dial back their harsh words for Democratic front-runner Hillary Clinton on Wednesday, and promised to press ahead in the face of her growing delegate lead.

At a rally here ahead of Maine’s caucuses this Sunday, Mr. Sanders pressed Mrs. Clinton to release transcripts of her paid speeches to Wall Street firms and mocked the idea that anything she said could have been worth the six-figure speaking fees she collected. He also reminded his audience...