By Nate Raymond

WASHINGTON (Reuters) - The U.S. Supreme Court on Monday turned away a novel case by Arizona seeking to recover billions of dollars that the state has said that members of the Sackler family - owners of Purdue Pharma LP - funneled out of the OxyContin maker before the company filed for bankruptcy in September.

The justices declined to take the rare step of allowing Arizona Attorney General Mark Brnovich to pursue a case directly with the Supreme Court on the role the drugmaker played in the U.S. opioid epidemic that has killed tens of thousands of Americans annually in recent years.

The lawsuit accused eight Sackler family members of funneling $4 billion out of Purdue from 2008 to 2016 despite being aware that the company faced massive potential liabilities over its marketing of opioid medications.

Brnovich argued that the national importance of holding those responsible for the opioid crisis accountable justified taking the case directly to the justices. Brnovich is a Republican.

The case is among the thousands filed by states, counties and cities seeking to hold Stamford, Connecticut-based Purdue, and in many cases the Sacklers, responsible for a U.S. opioid addiction crisis that since 1999 has resulted in more than 400,000 overdose deaths. The lawsuits accuse the company of deceptively marketing opioids by overstating their benefits and playing down the risks.

Purdue filed for Chapter 11 bankruptcy protection in September after reaching a tentative deal it values at $10 billion to resolve those cases.

Only half the states support the proposed deal, with many wanting the Sacklers to contribute more than the initial $3 billion the families pledged to pay.

A federal bankruptcy judge has placed a hold on all of the lower court and state court cases against Purdue. But Arizona declined to withdraw its Supreme Court case.

States opposed to Purdue's $10 billion settlement proposal in a later bankruptcy filing in October asserted that the amount of money the Sacklers received was $13 billion, more than triple the amount previously cited.

Lawyers for Purdue argued the bankruptcy court is a better forum than the Supreme Court to resolve Arizona's claims. In a brief, the states of Ohio, Alaska, North Dakota, Louisiana and Utah supported Arizona.

Brnovich's case relied upon language in the U.S. Constitution giving the Supreme Court "original jurisdiction" over disputes in which a state is a party, meaning states can file a lawsuit at the high court instead of litigating first in lower courts.

(Reporting by Nate Raymond in Boston; Editing by Will Dunham and Grant McCool)