Federal executions are set to resume in the next two weeks after the Supreme Court declined to hear a challenge to the new execution protocol on Monday. 

"The application for a stay of the mandate pending the disposition of the petition for a writ of certiorari presented to the Chief Justice and referred to the Court is denied. The petition for a writ of certiorari is denied," said the order for the case Bourgeois v. Barr on June 29. 

Four condemned inmates were arguing that their death sentences should be overturned due to the new execution protocol, which uses one drug instead of three in the process of lethal injection. 

The order was unsigned, but noted the dissent of "Justice Ginsburg and Justice Sotomayor [who] would grant the application and the petition for a writ of certiorari." 

Four justices are required to agree to grant a case certiorari. 

In July 2019, Attorney General William Barr announced that the Department of Justice and the Federal Bureau of Prisons would resume federal executions, and named five people who would be the first group of federal death row inmates to be executed.

"Under Administrations of both parties, the Department of Justice has sought the death penalty against the worst criminals, including these five murderers, each of whom was convicted by a jury of his peers after a full and fair proceeding," Attorney General William Barr said in a written statement at the time. 

Three of the executions are scheduled to take place on July 13. The last federal execution occurred in 2003. 

In November 2019, U.S. District Judge Tanya S. Chutkan issued an injunction delaying the executions until the Supreme Court ruled whether or not to take up the case. 

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In the injunction, Judge Chutkan pointed to a stipulation in the Federal Death Penalty Act requiring federal executions to be conducted "in the manner prescribed by the state of conviction." Two of the men sentenced to die had been convicted in states using the three-drug protocol.

According to the Death Penalty Information Center, there are currently 62 federal inmates on death row.

The four plaintiffs seeking to overturn their executions were all sentenced to death for multiple murders, all including the murder of children. 

In an interview with EWTN host Raymond Arroyo in June, President Donald Trump defended the use of the death penalty and claimed that his support of the death penalty did not impact his pro-life credentials. 

Arroyo asked Trump about whether presumptive Democratic presidential nominee Joe Biden is pro-life, noting that some Catholics claim Biden is a pro-life candidate because of his opposition to the death penalty and his efforts to end climate change, while claiming Trump is not.

"I am totally in favor of the death penalty for heinous crimes, ok? That's the way it is," the president said.

"I'm pro-life, he's not. And the Democrats -- look who he's putting on the court."

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"They want to put people on the court- you have no chance. So I'm pro-life, the Democrats aren't. Nobody can say that Biden is, look at his stance over the years," the president added, saying that in his view Democratic party operatives will advance a pro-abortion agenda if Biden is elected to the White House.

Pope Francis has called the death penalty a rejection of the Gospel and of human dignity, calling on civil authorities to end its use, as did Pope St. John Paul II and Pope Benedict XVI.

In 2018, the Catechism of the Catholic Church was revised to describe the death penalty as "inadmissible," citing the increasing effectiveness of detention systems, the unchanging dignity of the person, and the importance of leaving open the possibility of conversion.

The decision from the Supreme Court came on the same day it struck down a Louisiana law which would have applied new regulations to abortion clinics in the state. The law would have required abortion doctors to have admitting privileges at a local hospital.

The court found the rule posed substantial obstacles to a woman's access to abortion, without significant benefits to the safety of women. The suit against the law was brought by an abortion provider and two abortion doctors.