The US Supreme Court on Monday rebuffed a direct challenge to the constitutionality of the death penalty, refusing to hear an Arizona contract killer's argument that it amounts to impermissible cruel and unusual punishment and that American society has reached a consensus on the need to strike it down.

The justices also rejected death row inmate Abel Daniel Hidalgo's bid to strike down Arizona's death penalty law, which he argued makes too many defendants in the state eligible for capital punishment. Hidalgo fatally shot two men at a Phoenix body shop in 2001 after being paid $1,000 by a gang member, and pleaded guilty in 2015.

Under Arizona law, the death penalty can be meted out when the crime involved at least one of a list of 14 "aggravating circumstances," such as committing prior serious offenses or murdering for monetary gain. The number of aggravating factors has risen steadily in Arizona so that now 99 per cent of first-degree murder defendants are eligible for capital punishment, Hidalgo said in legal papers.

Liberal Justice Stephen Breyer, who has criticised the way the death penalty is used in the United States, wrote an opinion in this case saying Arizona's highest court wrongly applied US Supreme Court precedent and that the state's system "points to a possible constitutional problem."

99 per cent of first-degree murder defendants are eligible for capital punishment, Hidalgo said in legal papers.

But Breyer said the case lacked enough expert evidence or studies to properly review the constitutionality of the death penalty. Breyer was joined by fellow liberal Justices Sonia Sotomayor, Elena Kagan and Ruth Bader Ginsburg.

Hidalgo's attorney Neal Katyal, who argued that the death penalty violates the Constitution's Eighth Amendment prohibition on cruel and unusual punishment, expressed disappointment in the court's action.

In a Twitter post, Katyal said he remained convinced the Supreme Court "will come to recognise that the death penalty, as practically administered in this country, is unconstitutional."

The Supreme Court reinstated the death penalty in 1976 but the number of executions carried out in the United States has generally been declining since 2000. A majority of states have either outlawed capital punishment or no longer carry out executions.

A majority of states have either outlawed capital punishment or no longer carry out executions

Opinion polls have showed dropping public support for the death penalty, and several botched executions in recent years have added to societal concern over the practice. Hidalgo's lawyers also pointed to racial and regional disparities in how states impose the death penalty.

"In short," they wrote in a legal brief, "the death penalty has become a rare and 'freakish' punishment."

The Supreme Court has not seriously debated the constitutionality of the death penalty since the 1970s. The justices have imposed some limits in its application for juveniles and people with intellectual disabilities but have not accepted a case to decide the constitutionality of the death penalty itself.