At least 122 people have been executed by the Saudi government this year as the royal family intensifies a crackdown on dissenters.
"We submit that the anticipated outrage of those U.S. officials was not a proper consideration as a matter of law," a lawyer has argued in court.
The kingdom executed 146 people last year, the third highest figure of any country.
Capital punishment is "an attack on the inviolability and dignity of the person," according to the church's new ruling.
Dimitrios Pagourtzis was arrested May 18 and charged with capital murder of multiple persons, according to the Galveston County Sheriff's Office.
How many executions did the U.S. perform last year?
Officials in November 2017 struggled for 25 minutes to find a vein to shoot lethal injection drugs into his arm.
This comes as public support for capital punishment hits historic lows.
Capital punishment cases are down but five of the 23 executions this year still highlight the arguments of those who oppose the death penalty.
Ledelle Lee and Kenneth Williams received communion, while Marcel Williams and Jack Jones had more elaborate requests.
Hours before Thursday's planned execution, lawyers for Kenneth Williams filed a petition with the U.S. Supreme Court, seeking to halt the proceedings.
The double execution took place days after the state ended a nearly 12-year hiatus on executing prisoners on death row.
Arkansas, which has not carried out an execution in 12 years, planned to begin the lethal injections of at least six convicted murderers on Monday.
The deaths come after the assassination of one of the group's top militants last month.
Saudi Arabia has rejected a call to release Badawi and allow him to join his family in Canada.
The human rights watchdog called for an end to capital punishment for children and discrimination against girls.
Convicts will likely be put to death by firing squad on the prison island of Nusakambangan.
The state was unsuccessful when it first tried to execute Romell Broom in 2009.
Texas to execute Coy "Elvis Wayne" Wesbrook after spending 17 years on death row.