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The Clinton and Sanders campaigns are in discussions about when to hold a debate in April, but whether it is held before the critical April 19 New York presidential primary remains an open question.

The campaign for Senator Bernie Sanders of Vermont sent out a news release on Tuesday proclaiming that Hillary Clinton’s campaign had made “an agreement to debate him in New York before the state’s April 19 primary election.”

That, however, is not exactly what the Clinton campaign has said, at least publicly.

“We have expressed our willingness to debate in April, and the campaigns are discussing different options, including the option of a debate in N.Y. before April 19,” said Brian Fallon, the press secretary for the Clinton campaign, in an email on Wednesday.

The Democrats have held eight debates so far, and have agreed in principle to hold at least two more, including the one in April. The merry-go-round of who wants to debate and when has been a common theme in the Democratic primary, and Mr. Sanders’s push for one in April began in January, with a statement from Jeff Weaver, the Sanders campaign manager.

“Why won’t they debate in Brooklyn?” he said then. “What’s the matter with Brooklyn?”

He raised the issue again recently in a letter to Robby Mook, the Clinton campaign manager.

“Our campaign continues to believe that the people of New York deserve to have the debate held in their state, and that it should be held prior to the New York primary,” Mr. Weaver wrote. He later added, “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 in the polls.”

Last night, the campaign sent the letter to its supporters, asking them to “add their name” to their request to debate Mrs. Clinton before the New York primary.

The discussions are still a marked improvement from the start of the week, when Joel Benenson, the chief strategist for the Clinton campaign, suggested that there would be no debates unless Mr. Sanders changed his “tone.”

“Let’s see if he goes back to the kind of tone he said he was going to set early on,” Mr. Benenson told CNN. “If he does that, then we’ll talk about debates.”