The Maryland Senate resolution says the state's citizens "trafficked in human flesh," and denounced slavery's "unspeakable cruelties, including beatings, rape, and the forcible separation of family members from one another."
Anti-slavery resolutions proposed by Exum have failed the last three years.
A version in 2004 and 2005 supported congressional hearings and a federal commission for reparations for blacks, as well as educating Americans about the history of slavery.
Last year, language about reparations was stricken from the resolution in favor of the current version.
The Senate Judicial Proceedings Committee heard the resolution Thursday. If approved, the resolution would go to the full Senate for a vote.
Exum's efforts have the support of at least two Washington County state lawmakers.
Society no longer condones slavery, so if an apology "pushes it further behind us, then it's OK," said Sen. Donald F. Munson, R-Washington.
"Individuals who care, clear-thinking people, regret slavery," said Del. LeRoy E. Myers Jr., R-Washington/Allegany. "It sounds to me like another way of saying we're sorry."
Hagerstown recently had its own episode of racial forgiveness when it tried to make amends with baseball Hall of Famer Willie Mays.
Mays played his first professional game in the New York Giants' minor league system in 1950 at Municipal Stadium.
Because of segregation at the time, Mays, who is black, was forced to stay at a hotel apart from his white teammates. Also, Mays has said that insults, including a racial slur, were directed at him at the ballpark.
When Mays accepted an invitation to come back to Hagerstown in 2004, he also accepted the city's apology.
"You just don't hold that against a town because the town isn't the person who hurt you," he said that day.
The place where Mays stayed in 1950 was the all-black Harmon Hotel on Jonathan Street.
Bobby Harmon of Clear Spring, whose grandfather owned the hotel, understands and agrees with Mays' philosophy.
He said it takes two people for an apology to connect - the offender and the offended.
So when he hears that Maryland might express regret for slavery, he appreciates the sentiment, but he also sees the limit.
"The people that (should) apologize - they're all dead," Harmon said. "They missed their chance."
Instead, a resolution could lead to something bigger - a sense of understanding and compassion.
"You don't have any obligation to me," he says to those who might apologize. "What you can do is teach your children to allow them to see the tough times that black people have had ...
"This generation can look back and say, 'I'm going to be a little more sensitive. Look at how they were treated. Look at what they went through.'"
Myers, who is white and considers Harmon one of his closest friends, wondered whether a resolution, strongly worded as it might be, would heal wounds.
"When will society be forgiven?" he said. "Will this take care of it?"
It might, said Andy Smith, president of Brothers United Who Dare to Care, a Hagerstown black advocacy organization.
"Until we somehow come to a point of reconciliation and acknowledging that slavery was wrong and the impact it had on blacks - then we can look forward to change in the black community - that it wasn't our fault, what happened to us," he said.
The proposed resolution "shows responsibility, as well as sincerity," Smith said.