By Michael Levenson Globe Staff

Representative Edward J. Markey on Friday proposed holding two wide-ranging debates and four issue-specific debates with his Democratic Senate rival, Representative Stephen F. Lynch.

But Lynch’s campaign immediately rejected the offer, saying there should be at least four wide-ranging debates. In addition, Lynch’s camp complained that some of the advocacy groups Markey wants to host the issue-specific debates have been supportive of Markey’s bid for Senate.

The back-and-forth between the two Democratic rivals is part of an early tussle over the debate schedule as both men jockey for advantage in the public eye. Elizabeth Warren and Scott Brown had a similar scuffles while trying to negotiate their own schedule ahead of last year’s Senate race.

Markey, who initially said he did not want to negotiate the debate schedule through the news media, blasted out his proposed debate plan in a press release on Friday.

His schedule calls for one wide-ranging debate each in Springfield and Boston, sponsored by independent news organizations, and four issue-focused debates sponsored by news organizations and advocacy groups, to be held around the state. The topics, he said, could include education, jobs and the economy, public safety and national security, and “equal opportunity.”

“The voters deserve to hear the Senate candidates debate the issues that matter most to Massachusetts,” Markey’s campaign manager, Sarah Benzing, said in a statement. “With such a short primary, this proposed plan is aggressive and will bring the debate forum to as many voters as possible throughout the state.”

Lynch’s spokesman, Conor Yunits, quickly rejected the proposal, saying it was “not enough.” He said there should be at least four wide-ranging debates and the issue debates should not be sponsored by advocacy groups.