WASHINGTON—The federal government will resume executing death-row inmates after a 16-year hiatus, Attorney General William Barr said Thursday, countering a national trend that has brought a decline in the application of capital punishment.

The Federal Bureau of Prisons scheduled the executions of five condemned men who were convicted of killing children, undoing what essentially had been a moratorium on the federal death penalty during a Justice Department review of the drugs used to execute prisoners.

The...