WASHINGTON (Reuters) - A divided U.S. Supreme Court on Tuesday struggled for the second time over how to resolve whether immigrants detained by the U.S. government for more than six months should be able to seek their release while deportation proceedings unfold.

A majority of the justices appeared sympathetic to the idea that immigrants held long-term should be eligible for a bond hearing that would let them argue for their release.

Some of the court's conservatives seemed skeptical over whether such a hearing should be triggered automatically after six months, as a lower court had ruled. But conservative Justice Anthony Kennedy expressed concern about detainees being held for lengthy periods without any hearings as a result of government delays, suggesting he could side with the four liberals.

The issue has taken on increased importance as Republican President Donald Trump promises to step up deportations.

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The high court previously heard arguments in the case in November 2016 when it was shorthanded, and failed to issue a ruling. The court now has its full complement of nine justices, with Trump's appointee Neil Gorsuch restoring a 5-4 conservative majority. Gorsuch said little during Tuesday's argument to indicate how he would vote.

Conservative Justice Samuel Alito was among those who questioned why there should be a hearing triggered after six months. "Where does it say six months in the Constitution?" Alito asked.

Chief Justice John Roberts said a "more palatable option" would be to restrict claims to individual detainees who have been held for a long time rather than having a blanket rule requiring hearings for all.

Kennedy suggested that a "bright-line rule" that sets a hearing after six months could be an "easier" way to resolve the case.

The liberal justices were more openly sympathetic to the plight of immigrant detainees. Justice Stephen Breyer noted that even "triple ax-murderers" get bail hearings. Justice Sonia Sotomayor said that allowing people to be detained indefinitely was a sign of "lawlessness."

The long-running class action litigation brought by the American Civil Liberties Union includes some immigrants who were held at the border when seeking illegal entry into the United States and others, including legal permanent residents, who have been convicted of crimes.

The lead plaintiff is Alejandro Rodriguez, a legal immigrant from Mexico who was working as a dental assistant when he was detained for three years without a hearing. Rodriguez was placed in removal proceedings based on prior convictions for drug possession and joyriding. Although he was released eventually, the case brought on his behalf continued.

The justices are reviewing an October 2015 ruling by the San Francisco-based 9th U.S. Circuit Court of Appeals that upheld a lower-court injunction requiring a hearing after six months of detention. The justices potentially could issue a narrow decision sending the case back to lower courts without resolving the question of whether hearings are required.

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The Trump administration, like the Obama administration before it, argued that hearings can be permitted in certain instances but opposed a blanket rule requiring them.

A ruling is due by the end of June.

(Reporting by Lawrence Hurley; Editing by Will Dunham)