The dam held back water in Lake Delhi, a popular recreational site and home to hundreds of summer vacationers. Culver visited the area Sunday.
More than 10 inches of rainfall last week sent water cascading over the top of the earthen and concrete dam, and the force of the water eventually caused a 200-foot section to wash away.
Culver said the lake was a statewide asset and that he will do what he can to see that it is restored.
No one was hurt but about 50 homes and more than 20 businesses sustained major damage, The Des Moines Register reported.
It just makes your jaw drop," condominium owner Irv Janey said. "The lake's gone."
The Lake Delhi Recreation Association owns the dam, and the lake had several public boat landings and a pair of public beaches. Association president Jim Willey told the paper it did not have money to rebuild the dam.
"This is a real landmark, and I think it's in Iowans' best interests to save this lake," Culver said.
The dam was inspected in 2009, but only minor problems were noted.
If a new dam is built, it would have to comply with more stringent design requirements, the Iowa Department of Natural Resources said.