MIAMI, April 2 — Hinting that a remarkable turnaround in state policy was near, Gov. Charlie Crist said Monday that he hoped to persuade members of the Florida cabinet this week to end the practice of stripping convicted felons of their right to vote.

Florida is the most populous of three states whose constitutions require withdrawal of voting rights from all convicted felons, and it has the nation’s largest number of disenfranchised former offenders. The other two states are Kentucky and Virginia.

Felons in Florida who have served their prison and probation time can apply to have their voting rights reinstated, but the process can be time consuming and complex. Only a few hundred have their rights restored each year in Florida, where the American Civil Liberties Union says 950,000 remain disenfranchised.

Mr. Crist, a Republican, said that to win the support of some cabinet members, he might require former felons to pay whatever restitution they owe to victims before regaining their rights. Some civil rights groups, including the A.C.L.U., oppose such a compromise, but Mr. Crist said he had little choice.

“I want to do the doable,” he told reporters in Tallahassee. “I’m pushing as hard as I can to get as much as I can, but there’s a point beyond which I cannot go.”

Only a constitutional amendment could formally end the ban, but under state law, the governor and cabinet — who also make up the state clemency board — could grant blanket clemency to everyone who completes their sentence. Mr. Crist needs two of the three cabinet members to sign off on the plan.

Alex Sink, a Democrat who is the state’s chief financial officer, has said she supported modifying the ban. But Charles Bronson, the state’s agriculture secretary, and William McCollum, its attorney general, Republicans, have opposed it.

Former Gov. Jeb Bushwas adamantly against ending the ban, even though it contributed to problems in the 2000 presidential election. An unknown number of legal voters were removed from the rolls leading up to the election, after a company working for the state mistakenly identified the voters as felons. At the same time, some counties allowed felons to vote or turned away legitimate voters as suspected felons.

“I believe in my heart that everybody deserves a second chance,” Mr. Crist said. “And I’m hopeful that maybe later this week we’ll have an opportunity to restore civil rights for Floridians and give them that right to vote.”

Howard Simon, executive director of the A.C.L.U. of Florida, said he thought Mr. Crist was focused on persuading Mr. Bronson to soften his stance. He said Mr. Bronson wanted a list of exceptions, of violent criminals who would not be eligible for voting rights. Mr. Crist said he would not grant automatic restoration to murderers and sex criminals.

Terence McElroy, a spokesman for Mr. Bronson, said Monday: “Commissioner Bronson continues to believe that people who commit violent felonies ought to be treated differently than others who do not.”

Jenny Nash, a spokeswoman for Mr. McCollum, said he believed that “violent habitual offenders should not receive automatic restoration.”

Mr. Simon said it made no sense to require former offenders to pay restitution to regain their civil rights.

“How can they be expected to pay it if the state keeps putting barriers in the way of allowing them to be re-employed?” he said. “You can put people on a payment plan, but get them back to work first.”