An Alabama death row inmate is scheduled to die Thursday amid questions about his culpability in the deaths of three Birmingham police officers in 2004 and the wounding of a fourth.

Nathaniel Woods did not pull the trigger in the shooting. But he was convicted as an accomplice of the gunman, Kerry Spencer. Both were convicted of capital murder and sentenced to die.

Spencer has said he awoke to the police bursting into the Birmingham apartment where he dealt drugs, believed he was under attack and opened fire, Woods' lawyers argued Tuesday in an emergency appeal for a stay of execution filed in federal court. Officers were attempting to arrest Woods on an outstanding warrant, according to a summary of the case in an Alabama Court of Criminal Appeals' opinion. Woods said "OK, I give up" and was being held by officers when Spencer opened fire.

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Jefferson County prosecutors argued at his 2005 trial that Woods hated police and lured the officers into the Birmingham house so Spencer could kill them, essentially plotting their deaths. But Woods has "steadfastly maintained his innocence in any plan to entice the three officers into the house that day," the emergency appeal says.

Spencer, too, has insisted that he acted alone. In a handwritten letter delivered to a lawyer for Woods on Monday, Spencer wrote Woods is "100% innocent." (Read the full letter at the bottom of this story.)

"I know this to be a fact because I'm the person that shot and killed all three of the officers that Nathaniel was subsequently charged and convicted of murdering," wrote Spencer, whose appeals are still pending. "Nathaniel Woods doesn't even deserve to be incarcerated, let alone executed."

High-profile advocates including Martin Luther King III are also speaking out in support of Woods. In an open letter, King appealed to Alabama governor Kay Ivey to delay his execution. "Killing this African American man, whose case appears to have been strongly mishandled by the courts, could produce an irreversible injustice," King wrote. "Are you willing to allow a potentially innocent man to be executed?"

Celebrities like Kim Kardashian and rapper T.I. have publicly voiced support for Woods. "He did not fire a shot. He surrendered to authorities," T.I. wrote on Instagram. "All FAIR AND DECENT HUMANS SHOULD ACT NOW‼"

#NathanielWoods is scheduled to be executed in Alabama TONIGHT for murders he did NOT commit. Join the broad coalition- including members of the jury and relatives of the victims – in urging @GovernorKayIvey and @AGSteveMarshall to stay Nate’s execution. — Kim Kardashian West (@KimKardashian) March 5, 2020

Woods' family also delivered a letter to the governor on Wednesday asking to halt the execution. But Alabama Attorney General Steve Marshall urged Ivey to reject the "eleventh-hour request for a reprieve," according to the Associated Press.

"The evidence adduced at trial clearly shows that while Woods may not have pulled the trigger, he was a full participant in the officer slayings," Marshall wrote in a letter to Ivey. Marshall said Woods pointed to one of the officers so that Spencer could shoot him, according to the letter obtained by the AP.

This undated photo shows Nathaniel Woods. Alabama Department of Corrections/AP

Woods' current legal team says his previous representation was woefully inadequate, and potentially crucial evidence — including allegations of police misconduct and questionable witness testimony — have not been reviewed by appeals courts because of legal missteps.

Of crucial importance, his lawyer Lauren Faraino wrote in the emergency appeal, is a 2012 affidavit filed by Tyran "Bubba" Cooper, who said he operated the drug business from the home where the officers were shot. Cooper said in the affidavit he had previously paid two of the Birmingham police officers who died so that police wouldn't interfere with the drug business, Faraino wrote. But none of that information appeared in Woods' trial record.

"If the police officers had their own motives to be there at the Green Apartments that day and were not enticed there by Nathaniel, that would mean Nathaniel is innocent of capital murder," Faraino wrote.

Faraino said she contacted Cooper on February 15, who confirmed details about his payments to the two officers and said he was never contacted by Woods' attorneys. A Birmingham Police spokesman did not immediately respond to a request for comment from CBS News.

In addition, Faraino wrote she contacted Woods' girlfriend, Marquita McClure, on February 20. McClure told Faraino she had been intimidated into giving false testimony at Woods' trial that she had seen Woods and Spencer unloading weapons from a car into the apartments on the day of the shootings.

"In truth, she had not seen that that morning," Faraino wrote. "None of Nathaniel's post-conviction attorneys had ever contacted her about the case."

McClure also gave testimony at trial about Woods' alleged statements that he wanted to kill police officers but said she thought Woods wasn't serious, according to an Associated Press report at the time. According to that report, McClure said she told an investigator that Woods wanted to kill one of the officers but later admitted: "I made that up. I told y'all what you wanted to hear."

Woods' trial attorneys erroneously told him that he couldn't be convicted of capital murder without evidence he pulled the trigger, his appeals lawyers have said, leading him to turn down a plea deal that would have spared his life.

One of Woods' appeals relates to the method of execution — his lawyers say that the state withheld information when telling death row inmates to choose lethal injection or nitrogen hypoxia, an execution method not yet being implemented in the state. His lawyers argue state prison officials unlawfully sought to schedule the execution date sooner because he chose lethal injection.

Faraino told CBS News that Woods is "incredibly nervous" as he awaits the results of two outstanding appeals, but is starting to have some hope after seeing his story covered in the media.

"He is glad the truth of the story is finally being told," Faraino said.

Read the letter from Kerry Spencer about the role of Nathaniel Woods, below: