HOUSTON, United States

The US states of Texas and Alabama are scheduled to carry out two executions Thursday by lethal injection, despite a plea from the UN for the country to halt all executions.

"We are seriously concerned by the impending execution of two men in the United States of America," said UN Human Rights Office spokesperson Seif Magango, in a statement from its Geneva headquarters.

"This would follow the execution of six people in five different US states over a 12-day period last month," said Magango. "This rise in the rate of executions is deeply worrying."

The scheduled execution in Texas is garnering the majority of attention because of the unique circumstances surrounding the case, and if the lethal injection takes place Thursday, it would mark the first death sentence in the US for a conviction tied to shaken baby syndrome.

Defense attorneys for Robert Roberson, 57, said they have new evidence that shows their client did not murder his ailing two-year-old daughter, Nikki Curtis, by shaking her to death in 2003. She instead died of pneumonia-related complications, they said. Roberson has claimed his innocence for the last two decades.

A state parole board rejected Roberson's plea for clemency on Thursday, despite his attorneys presenting the new evidence. His last shot at delaying the execution is if Texas Gov. Greg Abbott grants a one-time 30-day reprieve without board recommendation, which Roberson's lawyers are requesting.

"We urge Governor Abbott to grant a reprieve of 30 days to allow litigation to continue and have a court hear the overwhelming new medical and scientific evidence that shows Robert Roberson's chronically ill, two-year-old daughter, Nikki, died of natural and accidental causes, not abuse," said attorney Gretchen Sween, in a statement.

The second execution involves Alabama death row inmate Derrick Dearman, 36, who was convicted of murdering five people in 2016, in addition to an unborn child of one of the pregnant victims.

Dearman admits he was high on methamphetamines when he wielded an axe to carry out the killings. He blamed his rampage on his struggle with drug addiction since he was a teen but said he accepts his fate come Thursday's scheduled lethal injection, despite filing an initial appeal which he eventually withdrew.

"I am guilty, plain and simple," Dearman told NBC News in April.

He made peace with his decision to withdraw his appeal and accept the judge's death penalty ruling.

"It's not fair to the victims or their families to keep prolonging the justice they so rightly deserve," Dearman wrote in letters sent to state officials asking for his execution to move forward, according to the USA Today newspaper.

Whatever the reasoning for either execution, the UN urged the US to "join the growing global consensus towards universal abolition of the death penalty" by "imposing a moratorium on executions," saying that evidence suggests that the death penalty has little to no effect in deterring crime.

"We oppose the death penalty, as a matter of policy, in all circumstances," said Magango. "It is incompatible with the fundamental right to life and raises the unacceptable risk of executing innocent people."