The survey, by the Hebrew University of Jerusalem and the Palestinian Center for Policy and Survey Research, shows 51 percent of Israeli respondents in favour of what is known as the two-state solution, down from 62 percent last June.
Support among Palestinians was also 51 percent, down from 54 percent a year ago.
Shortly after the previous survey, Israel fought a war in the Gaza Strip that killed some 2,200 Palestinians, most of them civilians, and 73 on the Israeli side, mostly soldiers.
"After forming a right wing government in Israel led by Benjamin Netanyahu, we asked both sides about their expectations for the future," a Hebrew University statement said.
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"The level of perceived threat on both sides regarding the aspirations of the other side in the long run is very high."
"Fifty-six percent of Palestinians think that Israel's goals are to extend its borders to cover all the area between the Jordan River and the Mediterranean Sea and expel its Arab citizens, and 25 percent think Israel's goals are to annex the West Bank while denying political rights to the Palestinians."