LITTLE ROCK — A federal judge Friday rejected claims by two condemned Arkansas inmates that their executions should be stayed because they have health conditions that would cause them to suffer severe pain and needless suffering during the state’s lethal-injection procedure.

Arkansas carried out its first execution in 12 years Thursday night when it put Ledell Lee to death for the 1993 slaying of Debra Reese of Jacksonville. Next week, the state intends to execute Marcel Wayne Williams and Jack Harold Jones on Monday and Kenneth Williams on Thursday.

Attorneys for Marcel Williams and Jones asked U.S. District Judge Kristine Baker to stay their executions, arguing that the men’s health conditions, including Williams’ obesity and diabetes and Jones’ diabetes, sleep apnea and use of medications including methadone, have decreased their sensitivity to sedatives like midazolam.

The state’s lethal-injection protocol calls for an inmate to be injected first with midazolam, then with the paralytic vecuronium bromide, a paralytic that stops the lungs from breathing, and lastly with potassium chloride, which stops the heart.

Attorneys for Williams and Jones argued that injecting the men with midazolam likely would not prevent them from feeling severe pain when the second and third drugs are administered.

Baker wrote in separate orders Friday that Williams and Jones could have presented their claims sooner, did not show that a method of execution significantly less likely to cause severe pain was readily available, and did not demonstrate they likely would be able to prove that Arkansas’ execution protocol would cause them severe pain and needless suffering.

Gov. Asa Hutchinson originally scheduled eight executions over an 11-day span this month, hoping to make use of the state’s supply of midazolam before it expires at the end of this month. The executions of Bruce Earl Ward, Don William Davis and Stacey Eugene Johnson, all of which were scheduled for this week, were canceled because of court stays.

The execution of Jason McGehee, which had been scheduled for next Thursday, also has been stayed. By Friday afternoon the state had not appealed that stay.