But the St. Louis businessman stopped short of calling for Akin to abandon his campaign for U.S. Senate.
"What he said was wrong and offensive, and he has admitted that," Spence said shortly after addressing a meeting of the University of Missouri College Republicans. "I'm really just choosing to run for governor and get 250,000 Missourians back to work. There's enough cooks in the kitchen now without me chipping in."
Last week, Akin came under fire for saying that "legitimate rape" rarely leads to pregnancy, a claim soundly rejected by the medical community. Akin has apologized for his remarks but is still facing repeated calls by national and state GOP leaders to drop out of the race.
Among those calling for him to step down are former Republican U.S. Sens. Jack Danforth, John Ashcroft, Kit Bond and Jim Talent, current Sen. Roy Blunt and GOP Republican presidential nominee Mitt Romney.
The concern among Republicans is not only that Akin could lose to incumbent Democratic Sen. Claire McCaskill -- a fear that has been fueled by recent polls -- but also that he may become a drag on the rest of the Republican ticket, including Spence, who is trying to knock off Gov. Jay Nixon.
Spence declined to speculate on the impact of Akin's presence on the ballot.
"Right now, I'm just concentrating on running for governor," he said. "I need to concentrate on things that are in my control."
Before Akin's rape comments, he joined Spence and the other statewide Republican candidates on a bus tour across Missouri. Spence also declined to say whether he thought he would campaign with Akin again this year.
"I'm running for governor. I'm just going to stick to that," he said.