Democratic candidate Roy Barnes said he opposes a mosque at the site.
"I believe the 9/11 site is hallowed ground and it is too painful and divisive to build a mosque there," Barnes said.
The Journal also asked Republican candidate Nathan Deal if he thought a mosque should be built near ground zero. Deal said Wednesday it wasn't his place to say.
"As governor, I don't want New Yorkers telling Georgians what to do with our land. I'll return the favor by staying out of their business," Deal said in an e-mail.
The proposed $100 million, 13-story mosque and Islamic center, which would be located two blocks from where the World Trade Center stood, has set off an uproar.
President Barack Obama has said Muslims have the right to build the mosque.
In the race for Georgia's junior senator, Republican incumbent Johnny Isakson of east Cobb sided with Barnes.
"I believe it is insensitive and inappropriate to build a mosque near the ground zero site," Isakson said.
Isakson's Democratic opponent, Michael Thurmond, did not respond to the question despite repeated phone calls and e-mails. Neither did U.S. Rep. David Scott (D-South Cobb), who is being challenged by Republican Mike Crane, a construction company owner.
Crane said the issue is about what is appropriate.
"Congress is legally permitted to vote itself a pay raise, but in our current economic situation, it would be wrong," Crane said. "In the same way, building a mosque near ground zero is not appropriate, decent or honorable. I believe the American people are ready to see their leaders take a stand and do the right thing, not because it is legal or permitted, but because it is the right thing."