US Representative Edward J. Markey proposed Friday to hold two wide-ranging ­debates and four issue-specific debates with his Democratic Senate ­rival, US 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.