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Senator Bernie Sanders of Vermont appeared on “The Tonight Show Starring Jimmy Fallon” on Tuesday to talk about climate change and income inequality and to leave no question that he thinks Donald J. Trump is a rabble-rouser.

A minute into the 10-minute interview, Mr. Fallon asked Mr. Sanders to respond to Mr. Trump’s recent proposal to bar all Muslims from entering the United States.

“Throughout history, you’ve had demagogues trying to divert attention away from the real issues,” Mr. Sanders said. “And what someone like Trump is trying to do is divide us up. A few months ago, we were supposed to hate Mexicans that he thinks are all criminals and rapists. Now, we are supposed to hate Muslims. And that kind of crap is not going to work in the United States of America.”

The crowd responded with loud applause that lasted several seconds. Mr. Sanders used the moment, with the crowd still clapping, to press issues at the core of his campaign. He said the United States faced enormous problems including a disappearing middle class and a corrupt campaign finance system.

“I think what the American people understand is that given the problems that we face, we’ve got to stand together, come together, and create a decent life for all of our people and stop this scapegoating of one group or another,” Mr. Sanders said.

For much of the segment, Mr. Sanders remained serious, reminding Mr. Fallon that the United States imprisons more people than any other country and that most of the country’s wealth is held by 1 percent of the population. He outlined for several minutes the need to take more seriously the effects of climate change, like rising sea levels, heat waves and increasingly severe droughts, and to push back against the oil and gas industry’s financial influence.

On Monday, Mr. Sanders released a 16-page climate change plan that called for an acceleration of the country’s transition away from fossil fuels, an increase in investments in clean and sustainable energy and changes to the country’s electric and transportation infrastructure.

“We owe it to future generations to move aggressively to save this planet,” Mr. Sanders said to Mr. Fallon and to applause from the crowd.

Mr. Fallon told Mr. Sanders that his goals would be tough to accomplish and asked how he would deal with any losses of jobs tied to fighting climate change.

“Transformation will cause problems,” Mr. Sanders said. “On the other hand, you’re going to create jobs if we move aggressively to energy efficiency.”

The late-night segment did have several lighthearted moments. Mr. Sanders laughed when Mr. Fallon reminded him that if he and Mr. Trump faced off in the general election, it would be “the battle of the New York boys.”

Mr. Fallon also poked fun at Mr. Sanders’s age — he is 74 — saying in his opening monologue that the senator plans to cut back on fossil fuels “because they are made from his high school friends.”

The interview ended in Mr. Fallon style with the two men playing “The Whisper Challenge.” To play the game, one person puts on headphones blasting loud music and the other person whispers a phrase in an effort to get the first person to understand what he is saying.

Mr. Fallon began wearing the headphones as Mr. Sanders laughed throughout the beginning, at one point saying, “Start again.” Finally, Mr. Sanders whispered “Iowa caucus.” But, Mr. Fallon screamed, “I-O-Cus,” “I got one,” and “I don’t wanna” before finally getting the phrase.

Mr. Sanders, however, had little problem guessing the phrase Mr. Fallon read when the roles reversed. It is a slogan Mr. Sanders hopes he’ll get to say in the general election: “Feel the Bern.”

