Updated: 13 MAY 19 12:31 ET

By Ariane de Vogue and Devan Cole, CNN

(CNN) -- An ongoing feud between Supreme Court justices over the application of the death penalty escalated again on Monday as the justices filed opinions in two death penalty cases and took the rare step of issuing public explanations to explain their bitter divide.

Death penalty cases are sometimes decided late at night, and the conservative justices on the court, especially Samuel Alito, Neil Gorsuch and Clarence Thomas, believe that inmates are engaging in last-minute appeals as a dilatory tactic. That dispute has been playing out in various cases all year long.

The orders further unmasked the tension building between the three conservative justices and liberals who think the justices should defer to lower courts when it comes to specific facts in individual death penalty cases, as well as Chief Justice John Roberts and Justice Brett Kavanaugh, who have also sided at times with inmates.

Monday's first case concerned Alabama inmate Christopher Lee Price, who challenged his planned lethal injection execution last month. The court denied his stay of execution in an opinion that triggered a nearly 3 a.m. dissent from Justice Stephen Breyer, joined by three other liberal justices, who asserted the planned sentence would be carried out in an "arbitrary way." Price's death warrant expired before the justices acted.

Thomas, Alito, and Gorsuch criticized their fellow justices for waiting beyond midnight to handle the effort to block the execution, resulting in what will be a seven-week delay.

Monday, Thomas said he wanted to "set the record straight," about how things were handled. He called Price's complaints "procedurally unremarkable and constitutionally acceptable," and said the issue is all about timing.

"Of course, the dissent got its way by default. Petitioner's strategy is no secret, for it is the same strategy adopted by many death-row inmates with an impending execution: bring last-minute claims that will delay the execution, no matter how groundless," Thomas wrote. "The proper response to this maneuvering is to deny meritless requests expeditiously."

"Whatever the right answer is to how the Supreme Court should handle 11th hour applications in capital cases, this isn't it," said Steve Vladeck, CNN Supreme Court analyst and professor at the University of Texas School of Law.

"The justices are clearly at loggerheads over what the rules should be when death-row inmates seek to challenge the method of their execution, but the right thing to do is to take a case on the merits, have full briefing and argument, and resolve the matter conclusively -- rather than continuing to snark at each other in separate opinions across different cases," he added.

According to the state, Price and an accomplice wielded a sword and a knife in 1991 and stabbed Bill Lynn, a minister, to death.

Awaiting execution, Price had recently argued that Alabama's lethal injection protocol would cause him severe pain and asked that the state use lethal gas as an alternative. Two lower courts had agreed to put the execution on hold, but after Alabama Attorney General Steve Marshall petitioned the Supreme Court, the majority agreed to lift the stay of execution.

Price is now scheduled to be executed on May 30, the Montgomery Advertiser reported.

Thomas went to great lengths to describe the murder that Price was accused of committing involving a minister, Bill Lynn, who was returning from church, and criticized Breyer for failing to include those details.

Thomas wrote that while "Bill died a slow lingering and painful death," 20 years after the conviction Lee was trying to delay his death.

"It is difficult to see his litigation strategy as anything other than an attempt to delay his execution," Thomas wrote.

Buddhist spiritual adviser

The second case involved Patrick Henry Murphy, who argued that he should not be executed in Texas because the state would not allow his Buddhist spiritual adviser to be present in the death chamber.

In that case, the court stayed Murphy's execution.

On Monday, Alito, joined by Thomas and Gorsuch, said he wanted to take the opportunity to explain why "the court's decision to grant the stay was seriously wrong."

Alito, picking up on the same theme from the Alabama case, said that Murphy was "egregiously delayed" in raising his claims.

"By countenancing such tactics, the court invites dispute," Alito wrote.

But Kavanaugh, joined by Roberts, wrote to explain their votes to allow the stay. They noted that under Texas' policy at the time, inmates who were Christian or Muslim could have their spiritual advisers in the room. But inmates of other religions could not.

"That discriminatory state policy violated the Constitution's guarantee of religious equality," Kavanaugh wrote. They noted that Texas has now changed the policy and no longer allows any religious ministers in the viewing room.

"In sum, this court's stay in Murphy's case was appropriate, and the stay facilitated a prompt fix to the religious equality problem in Texas' execution protocol," Kavanaugh said.