Nunn said in a prepared statement Friday that the pair should meet across Georgia in events hosted by non-partisan groups.
“Debates are going to be an important part of this race,” she said, a departure from the Democratic primary when she declined on multiple occasions to engage with several lesser-known candidates.
“I welcome the chance to engage in these dialogues in front of Georgia voters and hope my opponent will join me in this important process,” Nunn added.
Perdue’s campaign didn’t explicitly answer her invitation, which was issued only through a news release and not via direct contact with the Perdue campaign.
Instead, Perdue aide Derrick Dickey hammered Nunn for waiting until the general election to talk about debates.
“David participated in a dozen debates during the primary while Michelle Nunn dodged every debate except one to avoid taking a position on anything of substance,” Dickey said in an e-mail.
“For her to now talk about the importance of debates shows the complete disingenuousness of her campaign,” he wrote.
Dickey included a screen shot of a televised Democratic primary debate that featured an empty podium representing Nunn, alongside the three other Democrats she eventually defeated.
Nunn, Perdue and Libertarian Amanda Swafford are running to replace retiring Republican Sen. Saxby Chambliss.
The Georgia race will help determine which major party controls the Senate for the final two years of President Obama’s administration.
National Democrats view Nunn as their best shot at picking up a Republican seat this fall as Democrats try to maintain their majority.