A Republican group suing the Obama administration to end the military's "don't ask, don't tell" law asked the Supreme Court on Friday to overrule this week's decision by a federal appeals court to keep the policy in place while it considers the matter.

Justice Anthony Kennedy, who received the Log Cabin Republicans' filing, asked the Justice Department for its response. Kennedy is the justice responsible for appeals from the 9th Circuit; he can either rule on the case on his own or refer it to the entire court.

On Monday the U.S. Court of Appeals for the 9th Circuit ruled that the Pentagon can keep enforcing the ban on gay men and lesbians openly serving in uniform. The appeals court is set to hear arguments on the matter at a later date.

The Obama administration has argued that a court order to suddenly end the ban without first properly training military personnel could wreak havoc on the force and disrupt the ranks.

But the Log Cabin Republicans, which advocates for gay rights, argued in its filing that the only harm the government would suffer by lifting the ban is "entirely bureaucratic, procedural and transitory in nature," and "sharply outweighed by the substantial constitutional injury that service members will sustain" by keeping the policy in place.

"It is unfortunate the Obama Justice Department has forced the Log Cabin Republicans to go to the Supreme Court," LCR Executive Director R. Clarke Cooper said in a statement. Cooper was a State Department official during George W. Bush's administration and is a captain with the U.S. Army Reserves.

"The 9th Circuit order was arbitrary and an abuse of discretion and should be vacated immediately," said Dan Woods, the attorney representing LCR. "We continue to look forward to the day when all Americans can serve in our military without regard to their sexual orientation."

If the Supreme Court were to hear the case, Justice Elena Kagan would likely recuse herself, because she worked on the Justice Department's case strategy in her previous role as solicitor general. That would leave the case in the hands of just eight justices, five of whom are considered conservative and three considered more liberal.

Should the Supreme Court vacate the 9th Circuit's decision, then enforcement of "don't ask, don't tell" is once again ended pending any appeal by the Obama administration. If the high court declines to hear LCR's appeal, then the policy remains in place and the case remains under consideration by the appeals court.

Despite the work of several left-leaning gay rights organizations, LCR has emerged in recent weeks as one of the most high-profile organizations opposed to "don't ask, don't tell." The group has about 19,000 members nationwide.

It sued the Obama administration this summer to end the policy and caught the Pentagon off guard when a district court judge ruled the policy unconstitutional and ordered the military to stop enforcing it.

Cooper and other gay rights leaders met briefly last week with President Obama to discuss legislative efforts to repeal the ban. LCR is also lobbying five moderate Republicans to ensure any repeal legislation has enough support to pass the Senate during the upcoming lame-duck session.

Staff writer Robert Barnes contributed to this report.