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RENO, Nev. — Senator Bernie Sanders of Vermont told hundreds of volunteers gathered here on Saturday that his strong showings in Iowa and New Hampshire were not flukes.

“We surprised them in Iowa,” Mr. Sanders said to cheers. “We surprised them in New Hampshire. We are going to surprise them here in Nevada.”

While Mr. Sanders was expected to beat Hillary Clinton in New Hampshire, his 22-percentage point margin was still a resounding victory and one he hoped gives him a tailwind heading into next Saturday’s Democratic caucuses in Nevada.

He is hoping a win here will convince voters nationwide that he has broad appeal and can garner support from a more diverse electorate than in Iowa and New Hampshire, two predominantly white states. Mr. Sanders on Saturday focused his remarks on economic inequality, campaign finance reform and Wall Street regulation, topics at the core of his candidacy.

“People of Nevada know what Wall Street’s greed, irresponsibility, recklessness, and illegal behavior did,” Mr. Sanders said. “They did it all over this country but maybe no place more profoundly in terms of wrecking lives, than right here in Nevada.”

The senator also spoke to the crowd of 519 people about the importance of immigration reform and said he understands that many undocumented people are living in fear and need substantive legislation from the next president.

“Today, we have 11 million people in this country who are undocumented,” Mr. Sanders said. “I have met people throughout this campaign, young people with tears running down their cheeks, who are literally worried that they or their parents will be deported tomorrow, that they will be separated from their loved ones. Count me in as somebody who will lead the effort for comprehensive immigration reform and a path toward citizenship.”

Mr. Sanders added that if “Congress does not do the job that it is supposed to do, then we will use the executive powers of the White House.”

The senator also touted his immigrant roots Saturday, reminding his volunteers that he grew up watching his family struggle financially.

“My dad came to this country at the age of 17 without a nickel in his pocket from Poland, couldn’t speak English, never made much money,” Mr. Sanders said. “But he was as proud an American as you have ever seen because he saw what America gave to him and his kids, the kind of freedom and opportunity it gave.”

Later, at a forum in Reno, he took questions from the crowd, including one about how he would help “indigenous people,” or Native Americans.

“I have always stood with the oppressed people of this country and there are no people who have been more oppressed than the indigenous people of this country,” he said. “I will stand with you and do everything I can to bring dignity and respect and economic opportunity to those people who do not have it today.”

Mr. Sanders also hugged a woman who told him she was undocumented and feared she would be deported. “I will do everything that I humanely can to make sure you do not continue to live in fear,” he said.

He also reminded the crowd that he had voted against the Defense of Marriage Act, the 1996 law signed by President Bill Clinton that barred federal recognition of same-sex marriage, and which was largely overturned by the Supreme Court in 2013.