"Repentance comes from the heart," Mr. Perdue said. "I'm not sure about public apologies on behalf of other people as far as the motivation for them."
Lt. Gov. Casey Cagle expressed no such ambivalence. The Republican who presides over the state Senate said he's working on a proposal with members of that chamber.
"We're putting a strategy in place now to move forward with a resolution," he said. "We pass a lot of resolutions down here, and this is one that certainly has some merit."
A resolution acknowledging and apologizing for Georgia's role in the slave trade was initially expected Monday but could come later in the week instead.
A resolution, as opposed to a bill, would not require Mr. Perdue's approval.
Rep. Al Williams, the chairman of the Georgia Legislative Black Caucus, said the language was still being fine-tuned.
"To me, 'I'm sorry' is the simplest thing in the world, but we've kind of gotten bogged down in how we say 'I'm sorry,'" he said.
Members of the Georgia arm of the NAACP fanned out across the state Capitol for a day of lobbying on the issue.
The measure is being supported by state Senate President Pro Tem Eric Johnson, R-Savannah, who has been meeting with black leaders in the state.
The clamor for an apology for slavery comes as Georgia considers a measure that would officially designate April as Confederate History and Heritage Month.
Mr. Perdue said the issue is being handled by the Legislature and that he would watch what lawmakers do. But he cast the issue as a personal one and said the state should look forward, not back.
"I haven't run across anyone in Georgia who is not regretful and repentant of man's inhumanity when you talk about owning one another," the Republican governor said.
"Those of us in public office today, I think we're called to live our lives and inspire our citizens to live their lives so that our children and grandchildren have nothing to apologize for," Mr. Perdue said.
Last month, a resolution passed unanimously in Virginia expressing "profound regret" over slavery. Maryland's state Senate approved an apology resolution on Friday by a vote of 44-0.