“Hamilton,” the hit Broadway musical about colonial rebels shaping the future of an unformed country, took an even more political turn at the end of its performance on Friday night.

With Vice President-elect Mike Pence attending the show, the cast used the opportunity to make a statement emphasizing the need for the new administration of President-elect Donald J. Trump, a Republican, to work on behalf of all Americans.

As the play ended, the actor who played Aaron Burr, Brandon Victor Dixon, acknowledged that Mr. Pence was in the audience, thanked him for attending and added, “We hope you will hear us out.”

“We, sir — we — are the diverse America who are alarmed and anxious that your new administration will not protect us, our planet, our children, our parents, or defend us and uphold our inalienable rights,” he said. “We truly hope that this show has inspired you to uphold our American values and to work on behalf all of us.”

The audience broke out in enthusiastic applause and cheers.

Mr. Pence was leaving as Mr. Dixon began to read the statement from the stage. A show spokesman said that Mr. Pence stood in the hallway outside the entrance to the auditorium and heard the full remarks.

Mr. Pence had been seated in the center orchestra section, prominently visible to audience members. He appeared engaged throughout the show and applauded after most of its numbers, audience members near him said.

When Mr. Pence entered the Richard Rodgers Theater in Manhattan, he was greeted with a mix of clapping and booing, according to theatergoers who posted on Twitter.

The audience gave a standing ovation during the play at the line, “Immigrants, we get the job done,” one theatergoer, Christy Colburn, wrote on Twitter.

She added: “Crowd went NUTS at King George’s lines ‘when people say they hate you’ & ‘do you know how hard it is to lead?’ He had to stop the song.”

The statement that Mr. Dixon read was written by the show’s creator, Lin-Manuel Miranda, its director, Thomas Kail, and the lead producer, Jeffrey Seller, with input from cast members, Mr. Seller said.

“We had to ask ourselves, how do we cope with this?” Mr. Seller said. “Our cast could barely go on stage the day after the election. The election was painful and crushing to all of us here. We all struggled with what was the appropriate and respectful and proper response. We are honored that Mr. Pence attended the show, and we had to use this opportunity to express our feelings.”

Mr. Seller said that there was some discussion about whether it was appropriate to inject a political statement into the night, and that those involved decided to wait until the end of the performance. He said no cast members had skipped the performance to protest Mr. Pence’s appearance.

Mr. Trump has not seen “Hamilton” or inquired about tickets, Mr. Seller said, adding that the president-elect would be “welcomed to attend.”

The show’s politics — particularly its celebration of diversity and of the critical role immigrants played in the American Revolution and the early republic — stand in sharp contrast to some of the harsh language about immigrants that Mr. Trump used during the campaign and his focus on appealing to white men with statements about returning America to “the good old days.”

His first appointments to his cabinet and other major positions have been dominated by older white conservative men, with relatively few women or minorities under consideration for top-ranking positions at this point.

One of the most acclaimed Broadway musical in years, “Hamilton” has been especially celebrated by liberals for its resonant, provocative portrayal of America as a nation of immigrants — particularly with its casting of Hispanic or black actors in the roles of Alexander Hamilton, George Washington, Thomas Jefferson and other founding fathers.