The denunciation and admissions were made at the candidates' first debate held at the Missouri School of Journalism in Columbia Thursday.
Gibbons, the Republican Senate Pro Tem, advocated an extension of outgoing Attorney General Jay Nixon's No Call list to the use of political automated phone calls.
"They are offensive and drive people nuts," Gibbons said. "Even in my household, and in my parents' home, the volume of calls is unbelievable."
Koster, who is running on the Democratic ticket, said political automated calls should be eliminated altogether. If they are not, he said, the calls should provide a disclaimer identifying who paid for the call and providing contact information.
However, in response to a follow-up question posed by moderator and Associated Press reporter David Lieb, Koster admitted to using automated calls during the primary election season. He then said he would cease if the legislature called for an end to them.
"I did have a fairly aggressive primary where I needed to defend myself a fair amount," Koster said. "I would be happy to disarm if the legislature would call a truce to all this craziness."
Gibbons has not used automated calls during the primary season, but said he used them to promote community meetings regarding property tax law earlier this spring.
Gibbons said legislation to expand the state's no-call law restricting telemarketing has been in the Senate for several sessions.
"We have passed it," Gibbons said. "I have voted for it. It dies out in the House."
Additionally, both candidates said they would continue investigating Gov. Matt Blunt's office regarding access to deleted office e-mails that are public record.
After both declared their support for the Missouri Sunshine Law, Lieb brought up the "on-going battle between the attorney general's office and governor's office over access to e-mails," and asked if the candidates would continue with the investigation of the governor's office.
"There have been too many fights between the governor's office and the attorney general's office over the last four years," Koster said. "I hope that that era is over, and I will pledge to work in that direction. But the investigation will continue.
"I don't know what conclusion it comes to, but it should be brought to an appropriate and approved conclusion as quickly as possible," Koster also said.
Gibbons emphasized the cost of maintaining and bringing forward public documents.
"I don't understand how it could cost anything in the electronic age, at least going forward," Gibbons said. "Old records may be different, but going forward -- why can't they be produced at virtually no cost?
"That actually is not going to stop because I become attorney general," Gibbons also said. "It will be continued if the law and the facts warrant its continuation."
Other issues addressed in the debate, hosted by the Missouri Press Association and held on campus in the Missouri School of Journalism, included Internet crime, illegal immigration, eminent domain and methamphetamine lab seizures. There were few policy disagreements on those issues voiced by the candidates.