The death chamber and the steel bars of the viewing room are seen at the state penitentiary in Huntsville, Texas. REUTERS/Jenevieve Robbins/Texas Dept of Criminal Justice

The Supreme Court on Tuesday refused to hear an appeal asserting that the death penalty violates the U.S. Constitution's ban on cruel and unusual punishment filed by a Louisiana man convicted of fatally shooting his pregnant former girlfriend.

Two of the eight justices, liberals Stephen Breyer and Ruth Bader Ginsburg, said they would have accepted the case, repeating concerns about the death penalty's constitutionality they raised in a different case last year.

The justices, who have sharply disagreed among themselves over capital punishment, declined to consider the appeal brought by Lamondre Tucker, who was sentenced to death for the 2008 murder of 18-year-old Tavia Sills in Shreveport. Sills, nearly five months pregnant, was shot three times and her body was dumped in a pond.

Tucker, who is black, had argued in part that black males had an increased likelihood of being convicted of murder and sentenced to death in Louisiana's Caddo Parish due to endemic racism.

At the time of Tucker's conviction, a Confederate flag, symbol of the pro-slavery Southern states that lost the U.S. Civil War that ended in 1865, flew outside the county courthouse, his lawyers said in court filings.

Breyer wrote that Tucker "may well have received the death penalty not because of the comparative egregiousness of his crime, but because of an arbitrary feature of his case, namely geography."

"One could reasonably believe that if Tucker had committed the same crime just across the Red River in, say, Bossier Parish, he would not now be on death row," Breyer said.

Breyer's comments echoed similar remarks he made in June 2015 when the court upheld Oklahoma's lethal injection procedures.

The shorthanded court has steered clear of taking major cases since the February death of Justice Antonin Scalia, but even at full strength may not have accepted this one.

There is no indication the court is any closer to taking a case that would challenge the death penalty directly, with the court's two other liberals, Sonia Sotomayor and Elena Kagan, not joining Breyer's opinion. Four votes are needed for the justices to hear a case.

The pregnant Sills had told Tucker she believed he was the father. Later testing showed Tucker, 18 at the time of the murder, was not the father. The fetus did not survive.

The Supreme Court left in place a September 2015 Louisiana Supreme Court ruling that rejected Tucker's legal arguments and upheld his conviction and death sentence.

In the United States, 31 states have the death penalty and 19 do not.