Justice John Paul Stevens denied, without comment, Demjanjuk's plea to step into his case. The 89-year-old retired autoworker lives in suburban Cleveland, and he, his family and his lawyers have said he's in poor health and too frail to be sent overseas.
With his U.S. options dwindling, Demjanjuk's attorney in Germany made a separate appeal Thursday to a German court to block the deportation.
There was no immediate indication from Immigration and Customs Enforcement whether the agency would move promptly to deport Demjanjuk.
Messages seeking comment were left with an agency spokesman.
Earlier this month, the 6th U.S. Circuit Court of Appeals in Cincinnati denied Demjanjuk a stay of deportation.
"We are currently considering legal options including an appeal to the Supreme Court," his son, John Demjanjuk Jr., said in an e-mail to The Associated Press.
"Given the history of this case and no evidence of his personal involvement in even one assault, let alone a murder, this is inhuman even if a court says it is lawful," his son, John Demjanjuk Jr., said following the 6th Circuit loss.
An arrest warrant in Munich alleges he was a guard in Nazi-occupied Poland in 1943. Demjanjuk says he was a prisoner of war, not a camp guard.
His family says he's too old and sick to be sent to Germany, but the government says he gets around for his age and says surveillance video proves that.
A lawsuit was filed in Berlin "to stop the acceptance of my father as a deportee, Demjanjuk Jr. said in early May. The issue is whether Germany can accept him without having filed a formal request for extradition.
In the filing, provided to the AP, attorney Ulrich Busch argued that the government's approval of Demjanjuk's deportation is an "evasion of justice" because Germany has not filed a formal request for extradition.
Busch also asserts that German authorities have made no provisions for what would happen if Demjanjuk arrives in Germany but is acquitted or not brought to trial for medical reasons.
The Ukrainian native moved to this country in 1951 and became a U.S. citizen. But that citizenship was stripped 30 years later for lying about working in Nazi concentration camps, reports CBS News correspondent Cynthia Bowers. In 1986 he was deported to Israel, where he was sentenced to death for war crimes.
That conviction was stunningly overturned by the Israeli Supreme Court based on a misidentification of Demjanjuk and he was set free and returned to suburban Cleveland, reports Bowers. The new German arrest warrant was issued in March.
On April 14, immigration officers carried Demjanjuk in his wheelchair out of his home to deport him on a flight on an executive jet waiting on the tarmac. But within hours, the appeals court blocked the deportation while it reviewed his latest appeal.
As he was carried from his home, Demjanjuk had his head flung back, his mouth hung open and he moaned in apparent pain, infuriating relatives who said he had been promised a stretcher in consideration of his back pain.
The government responded by sending surveillance video to the court showing Demjanjuk walking unassisted to a doctor's office on April 6. The family said that Demjanjuk has good days and that the video didn't reflect his overall health situation.
Demjanjuk has said he suffers severe spinal, hip and leg pain and has a bone marrow disorder, kidney disease, anemia, kidney stones, arthritis, gout and spinal deterioration.