He said he sees the decline over the past few decades in executions throughout the country as a sign that more and more people are embracing a culture of life.
Society often tends to meet acts of violence with more violence, Estevez said.
"We need to heal that reaction- violence needs to be tempered by mercy," he said.
"We don't need to be engaged in vengeance, we don't need to be involved in killing. We need to be involved in restoration."
The bishop pointed to instances where the families of murder victims have asked that their loved one's killer not receive the death penalty.
"They who have been hurt the most are thinking and acting as Christians," he observed.
Estevez's letter lays out a recent history of the development of the Church's teaching on the death penalty.
The letter quotes a speech that Pope St. John Paul II delivered in St. Louis in 1999, in which he called for an end to the death penalty, calling it "cruel and unnecessary."
"The new evangelization calls for followers of Christ who are unconditionally pro-life: who will proclaim, celebrate and serve the Gospel of life in every situation," John Paul II said.
"A sign of hope is the increasing recognition that the dignity of human life must never be taken away, even in the case of someone who has done great evil. Modern society has the means of protecting itself, without definitively denying criminals the chance to reform."
John Paul II's 1995 encyclical Evangelium vitae notes that cases in which executing an offender is an "absolute necessity" are, thanks to improvements in the penal system, "very rare if not practically nonexistent," and reaffirms the Catechism's teaching that "bloodless means" are "more in conformity to the dignity of the human person."
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"Not even a murderer loses his personal dignity, and God himself pledges to guarantee this," John Paul II wrote.
Pope Benedict XVI, too, continued to support the limitation and eradication of the death penalty during his pontificate, Estevez writes.
During August 2018, Pope Francis ordered a revision to the Catechism of the Catholic Church, updating it to describe the death penalty as "inadmissible" and an "attack on the inviolability and dignity of the person."
Many Christians attempt to use Bible passages to justify the death penalty, but the death penalty as it exists in the United States, Estevez says, is particlarly contrary to a biblical view.
Dale Recinella, a Catholic death row chaplain in Florida and frequent collaborator with Bishop Estevez, used his skills as a lawyer to analyze how the death penalty, as applied in the US, compares to the requirements found in the Bible.
Recinella identified 44 requirements of the biblical death penalty when it was the law of the land in Israel. He found that the death penalty, in Florida and the US, scored zero out of 44 on the requirements of the biblical death penalty.