As protesters outside the court called for Mr Demjanjuk to be arraigned again, yesterday's hearing opened with a recommendation from Yosef Harish, the Israeli Attorney General, that the court should not launch new proceedings. He said he had taken the decision 'with a heavy heart'.
The judges then heard the arguments of six petitioners, including survivors of the Holocaust, the Los Angeles-based Wiesenthal Centre, which tracks down Nazis, and a far- right Israeli organisation, Kach, calling on the court to try Mr Demjanjuk on charges of being a 'Wachmann' - or SS guard - at two Nazi death camps in Poland: Sobibor and Flossenburg.
It was when Mr Demjanjuk was being tried for being 'Ivan the Terrible', the gas-chamber operator of Treblinka death camp, that the other allegations against him were made. He has denied them all along, but when it acquitted him of being 'Ivan the Terrible', the Supreme Court found he had lied in relation to the lesser allegations and that he had been a guard at Sobibor and Flossenburg.
The court decided not to convict him of these offences, however, because Mr Demjanjuk had had no opportunity to defend himself. It also decided not to order a new trial because of the time that had elapsed since Mr Demjanjuk's first trial began in 1987. Mr Harish said yesterday he could not endorse a new trial because there was a danger of double jeopardy - that Mr Demjanjuk would stand trial a second time on the same evidence, which would violate international principles of justice.
He also said the original extradition order which allowed Mr Demjanjuk to be brought to Israel from the US for trial in 1986 concerned Treblinka and not the other camps. Trying him a second time might therefore violate Israel's extradition treaty with the United States.
Since the Supreme Court ruling last month pressure has mounted for the Israeli justice system to find a means of re-trying Mr Demjanjuk. The 73- year-old car worker from Cleveland, Ohio, has meanwhile been waiting in an Israeli jail. The case has been complicated by parallel proceedings under way in the US, where Mr Demjanjuk is challenging the validity of the US extradition ruling.
Last week a Cincinnati court ruled that as Mr Demjanjuk had been acquitted of the charge for which he was extradited he should now be allowed to return to the US while the matter was properly examined.
This has opened up the possibility that, if the Israeli judges decide not to try him, Mr Demjanjuk may be able to return to the US. It had been expected that he would leave Israel for his native Ukraine, the only country so far to have offered him the chance to apply for citizenship.