Arkansas has wrapped up an aggressive execution schedule, putting to death its fourth inmate in eight days, hours after a last-minute motion to halt his execution failed before the US Supreme Court.

Kenneth Williams, 38, received a lethal injection on Thursday night at the Cummins Unit prison at Varner for the killing of a former deputy warden in 1999.

He was pronounced dead at 11:05pm, 13 minutes after the execution began.

Arkansas had initially held off on executing Williams, who was scheduled to die at 7pm local time, as officials awaited word from the Supreme Court. His death warrant was set to expire at midnight.

A few minutes after 10pm, the court ruled to deny the petitions, without elaborating on its decisions.

An Associated Press reporter who witnessed Thursday's execution said Williams lurched and convulsed 20 times during the lethal injection. A prison spokesman said he shook for approximately 10 seconds, about three minutes into the procedure.

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"I extend my sincerest of apologies to the families I have senselessly wronged and deprived of their loved ones," Williams said in a final statement he read from the death chamber. "... I was more than wrong. The crimes I perpetrated against you all were senseless, extremely hurtful and inexcusable."

Arkansas had scheduled eight executions over 11 days before one of its lethal injection drugs expires at the end of April - the nation's fastest pace since the Supreme Court reauthorised the death penalty in 1976. Courts issued stays for four of the inmates.

Among the four lethal injections was Monday's first double execution in the United States since 2000.

State officials have declared the string of executions a success, using terms such as "closure" for the victims' families.

The inmates have died within 20 minutes of their executions' beginning, a contrast from midazolam-related executions in other states which took anything from 43 minutes to two hours. The inmates' lawyers have said there are still flaws and that there is no certainty that the inmates aren't suffering while they die.

"The long path of justice ended tonight and Arkansans can reflect on the last two weeks with confidence that our system of laws in this state has worked," Governor Asa Hutchinson said in a statement issued after the execution. "Carrying out the penalty of the jury in the Kenneth Williams case was necessary. There has never been a question of guilt."

Arkansas scheduled the executions for the final two weeks of April because its supply of midazolam, normally a surgical sedative, expires on Sunday.

The Arkansas Department of Correction has said it has no new source for the drug - though it has made similar remarks previously yet still found a new stash.

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Court filings by Williams on Thursday afternoon followed two threads: that Arkansas executions this week were so flawed that there is little doubt Williams will suffer as he dies, and that he has an intellectual disability that would make him ineligible for execution.

He was sentenced to death for killing former deputy warden Cecil Boren after escaping from the Cummins Unit prison in a 1,800-litre barrel of hog slop in 1999. He left the prison less than three weeks into a life term for killing University of Arkansas at Pine Bluff cheerleader Dominique Hurd in 1998.

At the conclusion of that trial, he had taunted the young woman's family by turning to them after the sentence was announced and saying "You thought I was going to die, didn't you?"

After jumping from the barrel of kitchen scraps, he sneaked along a tree line until he reached Boren's house. He killed Boren, stole guns and Boren's truck, then drove to Missouri.

There, he crashed into a water-delivery truck, killing the driver, Michael Greenwood. While in prison, he confessed to killing another person in 1998.