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The US Justice Department has scheduled the executions of four federal inmates for the first time since 2003 after months of legal challenges.

Attorney General William Barr has ordered the executions to begin in July of the men on death-row, who were all convicted of killing children.

The inmates had accused the government of trying to hasten their execution and of not following proper methods.

Mr Barr on Monday said they had "received full and fair proceedings".

"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," .

"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."

Last July, Mr Barr directed the Bureau of Prisons to revise the government's execution protocol to use a single drug in order to resume the federal death penalty.

Executions were scheduled for last December, but the inmates issued legal challenges.

After an initial injunction last year from a district judge that stayed the scheduled executions, an appeals court reversed the order in April, ending a nearly two-decade hiatus on capital punishment for federal inmates.

The first inmate facing execution is Daniel Lee, a former member of a white supremacist group who killed a family of three in the 90s. His execution by lethal injection has been scheduled for 13 July.

The three other men - Wesley Purkey, Dustin Honken and Keith Nelson - will be put to death in July and August.

Purkey was found guilty of raping and murdering a 16-year-old girl, murdering an 80-year-old woman and kidnapping a child, resulting in the child's death. Honken was convicted of killing five people, including two children. Nelson pleaded guilty to the kidnapping, rape and murder of a 10-year-old girl.

Their attorneys have condemned the department's decision and are asking the US Supreme Court to step in.

Purkey's attorney said he is mentally ill and cannot understand why he is to be executed, . Honken's attorney said there was misconduct during his trial that needed to be reviewed, and Lee's attorney has accused the government of using "false evidence".

The justice department said all four have "exhausted appellate and post-conviction remedies, and no legal impediments prevent their executions".

The department on Monday also noted more executions will be scheduled at a later date.