JERUSALEM, Aug 2 (Reuters) - Palestinians facing eviction from Jerusalem"s flashpoint Sheikh Jarrah neighbourhood will have to wait for a ruling that will determine their fate after a discussion in Israel"s Supreme Court on Monday ended without a final decision. Four Palestinian families petitioned the high court to hear their appeal and eventually allow them to remain in their homes in the East Jerusalem neighbourhood where Israeli settlers claim ownership of the land. The judges have been trying to find a compromise that would defuse tensions over the case that helped trigger an 11-day war between militants in Gaza and Israel. One proposal was for the Palestinian families to recognize the Israeli ownership while they stay put as protected tenants. The families" lawyer, Sami Irshaid, said that proposal was unacceptable and that they were waiting for the Supreme Court to set a date to continue the hearings in the hope it leads to the reversal of a lower court ruling to evict. "We still hope that the court will approve our permission to appeal and accept the appeal and cancel the eviction orders against the four families that we argued on their behalf today in court," Ersheid told reporters outside the court in Jerusalem. Israel captured East Jerusalem in a 1967 war and later annexed it in a move not recognised by the United Nations. Sheikh Jarrah"s residents are overwhelmingly Palestinian, but Israeli settlers have moved into the area, gravitating toward a site revered by religious Jews as the tomb of an ancient high priest, Simon the Just. Israeli settlers say they have 19th century land documents to back their case and were backed by a lower court in October last year. Palestinians question the legitimacy of the documents and appealed. As a final Supreme Court decision loomed earlier this summer their campaign gained momentum, and international attention. That peaked amid heightened tensions over the Israel-Hamas war in May and Palestinian protests against Israeli police raids on Damascus Gate and Al-Aqsa mosque, the third-holiest site in Islam. The families last week said they received a new opinion from an Israeli legal expert supporting their position that they had full property rights to their homes because the Jordanian government granted them ownership when it was in control of East Jerusalem from 1949 to 1967. The case has assumed wider significance because Palestinians see Sheikh Jarrah as a symbol of dispossession and Israeli settlement expansion. Most countries regard Israeli settlements as illegal but Israel rejects this, citing historical and religious ties to the land on which they are built. The Israeli government framed Sheikh Jarrah as a property dispute, deploying riot police and water cannon to clear the area during protests.