PSR, in cooperation with Germany's Konrad Adenauer Stiftung, interviewed 1,270 adults in West Bank and the Gaza strip between December 3 and 6 for the poll, which had a margin of error of 3 per cent.
"In light of the tension in East Al-Quds and the increase in the level of mutual violence, 80 per cent (of Palestinians) support and 20 per cent oppose attempts by individual Palestinians to stab or run over Israelis in Al-Quds and the rest of the West Bank," the survey found.
Some 86 per cent believe that a disputed Al-Quds holy site known to Muslims as the Noble Sanctuary and to Jews as the Temple Mount is "in grave danger," and 56 per cent of Palestinians believe that Israel intends to destroy al-Aqsa mosque on the mount.
Politically, moderate Palestinian President Mahmoud Abbas and his secular Fatah party are still recovering from a drop in support following the July-August Gaza war.
If presidential elections were held today, the survey found, Ismail Haniyeh of the Islamist Hamas movement would win 53 per cent of the vote and Abbas 42 per cent (compared to 55 and 38 per cent three months ago.)
Hamas would win 36 per cent and Fatah 34 in legislative elections, said the poll - compared to 39 and 36 per cent three months ago.
Palestinian public belief that Hamas won the Gaza war dropped from 69 per cent three months ago to 66 in this poll.
Most Palestinians (58 per cent) are once again pessimistic about attempts to reconcile between the two rivals, Hamas and Fatah – after a unity government formed in June failed its promise to hold long overdue elections within six months.
Most of those (69 per cent) who heard Abbas' plan to set a deadline for ending the Israeli occupation through a UN resolution support it.
And most Palestinians reject the so-called “Islamic State Iraq and Syria” (ISIS), with three-quarters calling it a radical group that does not represent true Islam.