PHILADELPHIA — Democratic Party leaders scrambled on Monday night to rescue their convention from political bedlam as supporters of Senator Bernie Sanders erupted in boos, jeers and protests against Hillary Clinton after an email leak showed that party officials had sought to undermine Mr. Sanders in their race for the nomination.

Mr. Sanders, whose speech was shifted to a more prominent time in hopes of soothing delegates, struggled to unify the convention. His full-throated endorsement of Mrs. Clinton drew scattered boos, and his valedictory tone left some supporters in tears rather than rallying around the Democratic nominee. Another speaker, Michelle Obama, was far more electrifying, but while she drew affection from the crowd, her remarks did little to heal the lingering primary wounds.

The venting among Sanders supporters reflected months of pent-up frustration after he lost the nomination to Mrs. Clinton, whom they see as too accommodating to big business and Republicans. Mr. Sanders tried to intervene by sending a text message asking delegates “to not engage in any kind of protest on the floor,” while Clinton and Sanders campaign officials worked on the convention floor to mollify delegates who might be disruptive.

The tension reverberated from the floor of the hall to the stage. By 9:30 p.m., the outbursts were so loud and persistent that the comedian Sarah Silverman scolded the Sanders supporters who were shouting over her remarks.