The committee heard the bill last week. No action was taken.
Mooney voted against a similar ban in 2007, but said he would consider supporting a compromise bill this year that would ban capital punishment, except in cases when an inmate killed someone while in prison.
He has said in that case, the death penalty is the only way to "stop the killing."
Sen. George C. Edwards, R-Garrett/Allegany/Washington, said he is in favor of the death penalty for those crimes that are serious enough to warrant it.
The death penalty rarely is issued in Maryland, he said.
Eighty-six people have been put to death in Maryland since 1923, according to data provided by the Maryland Department of Public Safety and Correctional Services --Â the first year the state began keeping those records. The last death sentence was carried out in 2005, and there currently are five people on death row in the state.
Del. Christopher B. Shank, R-Washington, supports the death penalty and said there have been too many cases in Washington County that warranted punishment by death. He cited the case of Brandon T. Morris, who was convicted in 2008 in the slaying of Roxbury Correctional Institution Officer Jeffery A. Wroten of Martinsburg, W.Va. Morris was sentenced to life in prison without parole, but had been eligible for the death penalty.
Wroten's former wife, Tracey Wroten, said she still is bothered that Morris was not sentenced to death.
"My kids have to live every single day without their dad," she said.
The Wrotens had four daughters.
Tracey Wroten said all lives are precious, but there is a distinction between law enforcement officers and the general public. She said there should be a different, stricter penalty in place for those who kill law enforcement officers, such as her ex-husband.
Wroten said O'Malley wants to abolish the death penalty, but the majority of Marylanders do not.
Shank also mentioned the case of Douglas Pryor, who has been charged in the deaths of Alison Munson and Smithsburg Police Officer Christopher Shane Nicholson. The state is seeking the death penalty against Pryor for Nicholson's death.
"I believe firmly from talking to my constituents that the death penalty needs to remain an option," Shank said. "The overwhelming number of constituents I've talked to support it."
Del. Andrew A. Serafini, R-Washington, said he is not in favor of banning the death penalty in Maryland, but said the current system isn't working.
"I think there still needs to be a lot of work done," he said. "I don't think that repealing it right now makes a lot of sense."
Serafini said the lengthy, expensive appeals process hurts families of victims and the state. He said appeals can go on for decades, and when the family finally believes they have closure, another appeal is filed before the person can be put to death.
"The way it's working now, we really don't have a death penalty in this state," Serafini said.
Edwards said he's seen polls that show most Marylanders favor keeping the death penalty. However, he's unsure what a Senate committee discussing the issue will decide.
The bill could move out of committee with a favorable vote, or without one. In the Senate, that means lawmakers would have to bypass the committee vote by petitioning the bill to the full Senate, a move that would take the support of 16 senators in a chamber presided over by a death penalty supporter, Senate President Thomas V. Mike Miller.
Miller and O'Malley have called for a fair up-or-down vote on the issue.
However, Munson said he would not vote to end a filibuster in the Senate. He said there are people who commit such awful crimes they "remove themselves from the human race." For those who commit those crimes, the only fitting punishment is death, he said.