WASHINGTON — Hearing his first arguments in a death penalty case, Supreme Court Justice Brett M. Kavanaugh seemed open Tuesday to the arguments of a Missouri inmate who says his rare medical condition could result in severe pain if he is executed by lethal injection.

The court’s newest justice could hold the key vote in Russell Bucklew’s case. That’s because his eight colleagues split 4 to 4 earlier this year over whether to allow Bucklew’s execution to proceed. Justice Anthony M. Kennedy provided the fifth vote to spare Bucklew. Kavanaugh replaced Kennedy, who retired in July.

Bucklew, on death row for a 1996 murder, has said that a tumor in his throat is likely to burst during the lethal injection procedure, causing him to choke on his own blood. Bucklew argues that subjecting him to lethal injection would violate the Constitution’s ban on cruel and unusual punishment.

Among the questions Kavanaugh wanted answered was whether Bucklew would be lying flat during the execution, which Bucklew’s attorneys have said would be problematic.

Kavanaugh, who heard no death penalty cases in his 12 years as an appeals court judge, also asked whether there’s any legal limit on pain associated with an execution. The justice also aimed all his questions at the lawyer representing Missouri, which can be a sign at the Supreme Court that a justice is inclined to vote for the other side.

“Are you saying even if the method creates gruesome and brutal pain you can still do it because there’s no alternative?” Kavanaugh at one point asked Missouri’s attorney, D. John Sauer. He later asked Sauer: “Your opposing counsel said, even if everything goes according to plan, there will still be significant suffering. Can you respond to that?”

Bucklew is up against Supreme Court precedent in trying to get the justices to agree with him. The court has previously ruled that inmates challenging a method of execution have to show that there’s an alternative that is likely to be less painful. Bucklew has proposed that Missouri execute him by having him breathe pure nitrogen gas through a mask instead of by injecting him with a lethal dose of pentobarbital.

Bucklew says it is likely he would feel as though he’s suffocating for several minutes during a lethal injection execution. He says if the state uses nitrogen gas, he’d become unconscious within 20 to 30 seconds.

Missouri says no state has ever carried out an execution as Bucklew suggests, calling his proposal vague and untested. And the state says Bucklew would not suffer severe pain during a lethal injection execution because pentobarbital would make him unconscious within 20 to 30 seconds, likely sooner.

Chief Justice John Roberts suggested Bucklew’s proposed alternative wasn’t reasonable, asking “how can it be a reasonable alternative if it’s never been used before?” Roberts was one of the four justices who would have let Bucklew’s execution proceed earlier this year. Justices Clarence Thomas, Samuel Alito and Neil Gorsuch also would have allowed it to go forward.