Mr. Klein’s campaign told Crain’s New York on May 9 that the senator would not run on the Republican line in the June Primary. But Mr. Koppel then accused Mr. Klein of keeping open the possibility of running as a Republican in the September vote. Markos “Kos” Moulitas, the founder of the Daily Kos, wrote a post with the same message.

“Jeff Klein has proven he will say anything to win election, but then will do something completely different after the election to empower himself and disenfranchise Democratic voters,” Mr. Koppell said in a Monday statement.

But on Tuesday, Ms. Giove sought to set the record straight.

“We have decided that we are not taking the Republican line, period,” she said. “Not in June, not in September.”

Asked whether Mr. Klein might still run as an Independent, she declined to comment. New York law allows candidates to run under multiple party lines.

Mr. Samuels predicted a tough contest ahead, with Mr. Klein receiving a broad range of support from other elected officials and Mr. Koppell calling on individuals dissatisfied with the IDC-Republican coalition to support him. Mr. Samuels added that the Daily Kos’ fundraiser demonstrates the race resonates with people around the country.

“That just shows that people — not only in New York, but around the country — are very disappointed that New York is not leading the nation in passing progressive legislation,” he said.