The Supreme Court on Monday, over the objections of Justices Ruth Bader Ginsburg and Sonia Sotomayor, refused to take up a case challenging the federal government's new execution protocol, clearing the way for federal executions to resume in July.

Three executions scheduled days apart, beginning on July 13, would mark the first time the federal government has executed prisoners since 2003. A fourth inmate is scheduled to be executed in August.

Feb. 10, 2020: Attorney General William Barr speaks at the National Sheriffs' Association Winter Legislative and Technology Conference in Washington. His Justice Department will begin executing inmates in July after the Supreme Court refused to hear an appeal challenging the government's new lethal injection procedures. (AP Photo/Susan Walsh)

BARR ORDERS EXECUTION DATES FOR FOUR CONVINCED CHILD MURDERERS, AFTER TWO-DECADE HIATUS

"The American people, acting through Congress and Presidents of both political parties, have long instructed that defendants convicted of the most heinous crimes should be subject to a sentence of death," Attorney General William Barr said in a statement earlier this month. "The four murderers whose executions are scheduled today have received full and fair proceedings under our Constitution and laws. We owe it to the victims of these horrific crimes, and to the families left behind, to carry forward the sentence imposed by our justice system."

At issue in the appeal to the Supreme Court was an administrative law surrounding the federal government's new single-drug lethal injection procedure. Different states still used different protocols, and the inmates questioned whether the Trump administration’s new plan violates the Federal Death Penalty Act (FDPA), which says the state where a capital murder was committed should determine the method of execution.

The inmates scheduled for execution are: Danny Lee, who was convicted in Arkansas of killing a family of three, including an 8-year-old; Wesley Ira Purkey, of Kansas, who raped and murdered a 16-year-old girl and killed an 80-year-old woman; Dustin Lee Honken, who killed five people in Iowa, including two children; and Keith Dwayne Nelson, who kidnapped a 10-year-old girl who was rollerblading in front of her Kansas home and raped her in a forest behind a church before strangling the young girl with a wire.

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The inmates are separately asking a federal judge in Washington to impose a new delay on their executions over other legal issues that have yet to be resolved.

Fox News' Shannon Bream, Bill Mears, Adam Shaw and the Associated Press contributed to this report.