Senator Scott Brown’s campaign said Wednesday that he will accept an invitation to a third televised ­debate, the highest profile face-off yet, sponsored by a consortium of Boston-based news organizations.

The announcement followed Brown’s refusal to ­debate at the Edward M. Kennedy Institute, because Victoria Reggie Kennedy, widow of the late senator, ­declined his request that she stay neutral in the Senate contest. Kennedy, an active Democrat who is president of the institute’s board, had ­issued the debate invitation.