Former Sen. Bob Kerrey (D-Neb.) has returned fire from Karl Rove's American Crossroads group, seeking to reinforce his connections to the state.

Rove's group is running radio ads blasting Kerrey, who is mulling a Senate run in Nebraska but has lived in New York City for much of the last decade, as a carpetbagging liberal.

Kerrey has sent a letter back to Rove that was obtained by The Hill pointing out that he owns restaurants and a chain of gyms in the state.

"I heard your very funny radio ad and would like to invite you to come to Nebraska and have a burger with my family at one of my restaurants. Or better: Let's work out at one of my health clubs," Kerrey wrote to Rove. "I am certain you'll be glad you did."

The former senator is back in Nebraska talking to Democrats in the state about a run for the seat held by retiring Sen. Ben Nelson (D-Neb.), but has not publicly indicated whether he will run. He is likely Democrats' only chance to make the race competitive.