Authorities in Germany said Demjanjuk had been expected there by Monday.
Demjanjuk, a retired autoworker who lives in the Cleveland suburb of Seven Hills, kept out of sight Friday, as he has for years. He has argued that his deportation would amount to torture, given his frail health.
A German arrest warrant issued in March accuses the Ukrainian-born Demjanjuk of 29,000 counts of acting as an accessory to murder at the Sobibor camp in occupied Poland during World War II.
In Germany, Demjanjuk would have a chance to respond to the allegations before a judge. He denies involvement in any deaths.
In a three-page signed statement, Demjanjuk asked earlier in the week for asylum in the U.S. and said deporting him "will expose me to severe physical and mental pain that clearly amount to torture under any reasonable definition of the term."
"I am physically very weak and experience severe spinal, hip and leg pain, which limits mobility and causes me to require assistance to stand up and move about," the statement said. "Spending 8 to 12 hours in an airplane seat flying to Germany would be unbearably painful for me."
In the statement, Demjanjuk said he suffers from a bone marrow disorder, kidney disease, anemia, kidney stones, arthritis, gout and spinal deterioration.
His attorney, John Broadley, said a government physician examined Demjanjuk on Thursday to determine his ability to travel and there was "dramatic evidence" of his back pain. Broadley submitted a portion of the exam videotape to the government on Friday as part of his argument against deportation.
In his statement seeking asylum, Demjanjuk questioned Germany's motive in seeking his deportation and suggested the German government was trying to make up for lax earlier pursuit of war criminals.
"It is possible that the German authorities see a prosecution of me as means to draw attention away from their past approach," the statement said.
A German Justice Ministry spokeswoman, Eva Schmierer, declined to comment on Demjanjuk's statement.
Demjanjuk's son, John Demjanjuk Jr., said in interview that the family was relieved.
"There's a sense of relief that we don't have to deal with the trauma for him and for our family and for the many, many people that have been sympathetic to his cause for many years, believing in his innocence and believing that he was a victim of the war as much as anyone else was but he's still in pain. He's still ill," he said.