"It is unfortunate that a USA district judge has chosen to side with the convicted prisoners in one of their many last-minute attempts to delay justice", Jude Deere, an office spokesman, said.
The state had planned to execute the eight inmates before its supply of a lethal injection drug expires at the end of April.
Ward's decision "to delay a month to initiate this case, leaving the circuit court and this Court on appeal only 15 days to act, weighs in favor of the Respondents", said Ms. Rutledge.
The attorney general's office says it will respond to the filing after full arguments are put before the appeals court.
All eight executions in Arkansas were on hold as of Sunday, but if they resume this week as originally planned, state officials want convicted murderer Bruce Earl Ward back on the list.
A different federal judge has issued a stay for an inmate who won a clemency recommendation from the state's Parole Board, while the state Supreme Court has issued one for another inmate pending more mental health tests. A state court judge on Friday blocked Arkansas from using one of its three lethal injection drugs until he can determine whether it was obtained properly, and a federal judge on Saturday issued stays of all the executions. Any decision there would likely also be appealed to the U.S. Supreme Court.
Lawyers for the Arkansas attorney general's office are reportedly working to overturn recent decisions that halted the state's quick plan to execute eight inmates before the end of the month. Both men are scheduled for execution April 17, 2017.
FILE- In this January 4, 2017, file photo Arkansas Gov. Asa Hutchinson speaks to members of the press during a Q&A session in Little Rock, Ark.
Nine death row prisoners brought the case to the state, arguing that midazolam could expose them to "severe pain". This photo provided by Sherry Simon shows Pulaski County Circuit Judge Wendell Griffen taking part of an anti-death penalty demonstration outside the Governor's Mansion Friday, April 14, 2017 in Little Rock, Ark.
People gather at a rally opposing the state's upcoming executions, on the front steps of Arkansas' Capitol, Friday, April 14, 2017, in Little Rock, Ark.