The survey was released Wednesday, hours before US Secretary of State John Kerry's return to the region. Kerry is trying to forge agreement on the outlines of a peace deal, but gaps remain.
In the poll, 63% of 601 Israelis and 53% of 1,270 Palestinians surveyed said they back a two-state solution. Support dropped to 54% and 46%, respectively, when respondents were asked about specifics of a two-state deal.
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The Israeli poll, by an Israeli university, had an error margin of 4.5 percentage points. The Palestinian survey, by a West Bank think tank, had an error margin of 3 percentage points.
During his tenth round of Mideast shuttle diplomacy, US Secretary of State John Kerry will try to get Israel and the Palestinians to agree to the outlines of a final peace agreement, but does not expect a "big breakthrough" during his trip to the region this week, a senior State Department official said Tuesday.
Kerry will test ideas for breaching gaps between Israel and the Palestinian Authority, according to the official, who spoke on condition of anonymity to brief reporters ahead of Kerry's departure on Wednesday. But the official tempered expectations, saying a "big breakthrough" was not likely during the trip.
After 20 rounds of talks Kerry wants to intensify talks further. "We have established very well where the gaps are, but also generated some ideas that could help to serve as ways of bridging those gaps. The secretary's trip this time is to start to test those ideas with the two leaders," the official said.
The official said Kerry "has a real sense of urgency, a real sense of need to strike while the iron is hot. We consider the iron to be hot."
"We're going to work assiduously to try to reach this framework agreement as soon as possible," the official added.
Any agreed framework would not be a signed document, but would address all core issues, including the borders between Israel and a future Palestine, security, Palestinian refugees and conflicting claims to the holy city of Jerusalem, the official said.
The official also said if the parties agreed on a framework for negotiating a final peace deal, it might not be made public to avoid exposing the leaders to political pressures at home.
A framework might not even be enough to ensure a subsequent face-to-face meeting between Israeli Prime Minister Benjamin Netanyahu and Palestinian President Mahmoud Abbas , an indication perhaps that wide gaps remain.
Associated Press, Reuters contributed to this report
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