By Lawrence Hurley

WASHINGTON (Reuters) - In a last-ditch effort to revive a White House plan to protect up to 4 million immigrants from deportation, the Obama administration on Monday asked the U.S. Supreme Court to rehear a case on which the eight-member court was split 4-4 last month.

The June 23 high court decision left in place a lower court ruling that blocked the plan, which has never been in effect. The court is currently one justice short following the death of Justice Antonin Scalia in February.

In a filing, the Justice Department asked the court to take a second look at the case once it has a full complement of nine justices. It is unclear when that would be, as the Republican-controlled U.S. Senate has declined to act on Obama's nominee, appeals court judge Merrick Garland. As such, even if the Supreme Court was to grant the request, it is unlikely to rule on the case until well after Obama leaves office in January.

Acknowledging that the high court rarely rehears cases, Acting Solicitor General Ian Gershengorn said the immigration case is unique because the court could not in future take another case to resolve the issue if the plan is blocked. The high court "should be the final arbiter of these matters through a definitive ruling," he wrote.

Obama unveiled his plan in November 2014. It was quickly challenged in court by Republican-governed Texas and 25 other states that argued that Obama overstepped the powers granted to him by the U.S. Constitution by infringing upon the authority of Congress.

"Because we are right on the law, we have prevailed at every stage in this case, and we are confident that we will continue to prevail," said Marc Rylander, a spokesman for Texas Attorney General Ken Paxton.

As a result of the high court's 4-4 split, a 2015 lower-court ruling invalidating Obama's plan was left in place. The plan never was implemented because the lower courts had blocked it.

The plan was tailored to let roughly 4 million people - those who have lived illegally in the United States at least since 2010, have no criminal record and have children who are U.S. citizens or lawful permanent residents - get into a program that shields them from deportation and supplies work permits.

Obama took the action after Republicans in the U.S. House of Representatives killed bipartisan immigration legislation that was passed by the Senate in 2013.

(Reporting by Lawrence Hurley; Editing by Jonathan Oatis)