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Senator Bernie Sanders of Vermont challenged Hillary Clinton on Sunday to a debate in New York before the state’s primary on April 19 and expressed concern that Mrs. Clinton might not debate him now that she is far ahead in the race to win the Democratic nomination.

Appearing on NBC’s “Meet the Press,” Mr. Sanders said he wanted to have a debate in “New York City, upstate, wherever, on the important issues facing New York and, in fact, the country.” The Democrats have held eight debates so far, the last one on March 9 in Miami, and the two campaigns pledged to hold an additional debate in April and another one in May before the final primaries in June.

Asked by Chuck Todd, the host, if he was worried that Mrs. Clinton would not debate him again, Mr. Sanders replied, “Yeah, I do have a little bit of concern about that. But I certainly would like to see a debate in New York State.”

A Clinton campaign spokesman declined to comment about the debate proposal on Sunday.

Mr. Sanders, fresh off three caucus victories on Saturday, is seeking every opportunity to keep his chances alive despite Mrs. Clinton’s delegate lead, which has not significantly changed. Sanders advisers consider New York to be a crucial battleground; if Mr. Sanders could beat Mrs. Clinton in her home state, it would be a humiliating blow and – perhaps more than any other contest – cast doubts on her strengths as a general election nominee. Yet Mr. Sanders would need a landslide victory in New York to start chipping away at her lead in delegates.

Jeff Weaver, Mr. Sanders’s campaign manager, sent a letter on Sunday to his counterpart in the Clinton campaign, Robby Mook, asserting that the two teams had agreed to have a debate in California in May but had not yet come to terms on an April showdown. Mr. Weaver argued for New York as the location, noting that it had the most delegates at stake in April, and then adopted a taunting tone, suggesting that Mrs. Clinton was afraid to debate Mr. Sanders.

“It is difficult to understand your motivation,” Mr. Weaver wrote. “Can you please explain why New York should not host the April debate? Is the Secretary concerned about debating before the people who twice elected her to the U.S. Senate? Perhaps there is some tactical advantage you are seeking by avoiding a debate in New York but I would remind you that Senator Sanders agreed to debate the secretary in New Hampshire when he was well ahead.” Mr. Sanders ended up winning the New Hampshire primary in a rout; Mrs. Clinton had double-digit leads over Mr. Sanders in some recent New York polls.

Advisers to Mrs. Clinton have said recently that they are waiting for the Democratic National Committee to weigh in on the April and May debates. But party officials have said they are waiting for the campaigns to agree to a plan, and Sanders advisers scoffed at the notion that the Clinton camp could not negotiate for themselves. Mrs. Clinton has not dismissed the idea of more debates, unlike Donald J. Trump, the leading Republican candidate, who pulled out of one that had been scheduled for last week.