WASHINGTON — The Supreme Court on Monday turned down a request that it take a fresh look at whether the death penalty is constitutional anywhere in the nation.

The court also refused to consider a narrower question in the same case: Whether Arizona’s capital sentencing system, which appears to make virtually all murderers eligible for the death penalty, violates the Constitution.

In a 2015 dissent, Justice Stephen G. Breyer had urged his colleagues to revisit the death penalty, saying that “it is highly likely” that it violates the Eighth Amendment, which bars cruel and unusual punishments. He said that there was evidence that innocent people have been executed, that death row exonerations were frequent, that death sentences were imposed arbitrarily and that the capital justice system was warped by racial discrimination and politics.

Only Justice Ruth Bader Ginsburg joined the 2015 dissent, and the issue does not seem to have gained traction in the intervening years.