"It's a two-way street, the Clinton people are also going to have to listen to what these people are fighting for," Sanders said during an interview on CNN's "New Day."

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"The Clinton people are going to have to say, well, maybe Bernie has a point that we should not be the only major country on earth not to guarantee healthcare to all people or have paid family or medical leave. And maybe, yes, the billionaire class should start paying their fair share of taxes, and maybe, yes, we should break up Wall Street," he said.

"It's not me. I don't control millions of people, but the Clinton campaign is going to have to make the case to those young people that in fact they are prepared to stand up for some real, fundamental changes in this country, and that's the case they have not yet been able to make," Sanders said. The Vermont senator trails Clinton by nearly 250 pledged delegates, and Clinton holds a bigger edge among the superdelegates, who have indicated support for his campaign. The two have sharpened their barbs heading into Tuesday's New York primary, where Clinton is hoping to end Sanders's winning streak and move closer to the necessary 2,383 delegates to lock up the nomination. Clinton has 1,289 pledged delegates and 469 superdelegates, compared to 1,045 delegates and 31 superdelegates for Sanders, according to The Associated Press delegate tracker Sanders maintained Monday that while Clinton is the Democratic front-runner and has moved to the left on some issues during the campaign, she has not yet made the case to win over his supporters. "They're very good at rhetoric, and certainly she has moved to the left in this campaign in response to many of the initiatives that we have brought forth," Sanders said. "The average person understands that when you collect such large amounts of money from Wall Street and other special interests, they have their doubts whether the Clinton people will stand up to these powerful forces," he added.

Also in the interview, the self-described democratic socialist dismissed those who argue his proposals are unrealistic.

"Change takes place when people stand up and fight for change," Sanders said. "I believe everything we're talking about — nothing is radical, these ideas exist in other countries; they have existed in the United States."

— This report was updated at 11:03 a.m.