Almost 52 per cent of Palestinians in the West Bank and East Jerusalem do not want the current wave of knife attacks against Israelis to continue, according to an opinion poll published Sunday.
In the Gaza Strip, by contrast, more than three quarters of Palestinians support the latest intifada (uprising) and want it to continue, said the Jerusalem Media and Communications Centre.
Since early October, Palestinians have launched more than 200 knife attacks - including attempted attacks - against Israelis, the Israeli Foreign Ministry says.
Almost 200 Palestinians - the vast majority of them knife attackers - and 30 Israelis have been killed.
The attacks protest perceived Israeli violations - vehemently denied by Israel - at a disputed Jerusalem holy site, as well as the ongoing occupation.
Israel blames the violence on inflammatory rhetoric by radical Muslim leaders, who call on youths to stab Jews to "defend" al-Aqsa Mosque and who glorify the attackers as "martyrs" and "heroes."
Palestinians blame the violence on oppression and deep disillusion with peace negotiations, a last attempt at which collapsed two years ago.
The knife attackers have come mostly from the West Bank and East Jerusalem, as it is much harder to reach Israeli targets from the Gaza Strip, other than with rockets.
But tensions in the Gaza Strip have also been intensifying. The Israeli military said that seven rockets have been launched at Israel from Gaza since the beginning of the year.
The rockets have been fired mostly by hardline Salafists - not by Hamas, which has observed a ceasefire brokered to end the 2014 Gaza war.
Some 2,200 Palestinians and 70 Israelis were killed in that 50-day conflict.
"Our policy regarding the Gaza Strip is clear. Israel will not accept rocket fire of any kind from the strip at its territory," Israeli Prime Minister Benjamin Netanyahu told his cabinet Sunday.
Israel "holds Hamas responsible for all firing from the Gaza Strip toward Israel," he said, because the Islamist group controls the coastal enclave and "should prevent such firing."
A 10-year-old Palestinian boy and his 6-year-old sister were killed Saturday, when Israel bombed a Hamas base in the northern Gaza Strip. Shrapnel hit the siblings' nearby home as they were sleeping.
Israel bombed four sites of the Islamist movement in de facto control of the Strip, retaliating four rockets launched from Gaza late Friday.
"Our patience for violations by the occupying power has its limits," warned the Qassam Brigades, Hamas' armed wing.