The 21-year-old has admitted playing a part in the bombing but claims his brother Tamerlan, who died in a subsequent fight with police, was the driving force in organising it.
The jury are currently deliberating on a verdict in regards to 30 federal charges. If they find him guilty they will be given more evidence before deciding whether he should be given a prison sentence of life or the death penalty.
In a statement the Church leaders, led by Archbishop of Boston Cardinal Seán O'Malley said: "As Pope Francis has recently stated, '[The death penalty] is an offense against the inviolability of life and the dignity of the human person. When the death penalty is applied, it is not for a current act of oppression, but rather for an act committed in the past. It is also applied to persons whose current ability to cause harm is not current, as it has been neutralized - they are already deprived of their liberty'.
"The defendant in this case has been neutralized and will never again have the ability to cause harm. Because of this, we, the Catholic Bishops of the Commonwealth of Massachusetts, believe that society can do better than the death penalty.
"As the Bishops of the United States said in their 2005 statement A Culture of Life and the Penalty of Death, 'no matter how heinous the crime, if society can protect itself without ending a human life, it should do so.' We believe these words remain true today in the face of this most terrible crime."
The 2013 attack killed three people and injured 264 others. The jury has heard evidence from 96 witnesses over the past month as they try to come to a verdict.