Palestinian groups, from President Yasir Arafat's Fatah to resistance groups Hamas and Islamic Jihad, emerged from four days of talks in Cairo on Sunday unable to agree to halt the attacks.
But Quraya, who made a suspension of attacks his priority in an attempt to restart peace talks with Tel Aviv, maintains an eventual agreement is still a possibility.
On Monday, members of Yasir Arafat’s Fatah faction said they would try to persuade resistance movements to change their minds.
Palestinian Foreign Minister Nabil Shaath insisted there was "a general readiness" for a truce.
Israeli military actions
He said Quraya would meet the Israelis to see if they were willing to reciprocate and halt military actions.
The foreign minister said the resistance groups had told Quraya to "go continue your negotiations with the Israelis, if you feel they are ready to reciprocate, come back".
Hamas, which is spearheading the Intifada, said it was willing to halt attacks against civilians in Israel, but would continue striking Jewish settlers and soldiers.
And Nafiz Azzam, a spokesman for Islamic Jihad in Gaza, said the groups would not go along with a comprehensive truce without Israeli guarantees to also halt invasions.
"It was difficult for us and other factions to accept a new truce without guarantees from the Israeli side, because the previous truce failed in the same way"
He noted a ceasefire initiated by Palestinians in June fell apart when Israel kept up attacks.
"It was difficult for us and other factions to accept a new truce without guarantees from the Israeli side, because the previous truce failed in the same way," he said.
Azzam said neither Quraya nor Umar Sulayman, the Egyptian intelligence chief who mediated the talks, presented any Israeli guarantees.
Hamas, along with four other factions, wants Israel to fulfil three conditions.
These include lifting crippling blockades around Palestinian cities and towns, ending raids and house demolitions in the occupied Palestinian territories, and freeing all detainees being held in Israeli prisons.
But some commentators argued on Monday that Quraya was chasing an agreement which was desired neither by Israel nor the Palestinian groups.
They said both were already curbing their activities and achieving a more sustained period of calm than under the previous failed truce.
However, Israel is still officially encouraging Quraya to continue his efforts.
"We do not judge Quraya. He is not the bad guy, the bad guys are the terrorists. At the very moment these organisations stop their terrorism, we will stop our military operations," Israeli government spokesman, Avi Pazner said.
"A truce is absolutely necessary. There has not been one moment when terrorist organisations did not try to perpetrate their murderous actions, and it is only because of the quality of our security services that we have seen a period of quiet"
Israeli government spokesman
"A truce is absolutely necessary. There has not been one moment when terrorist organisations did not try to perpetrate their murderous actions, and it is only because of the quality of our security services that we have seen a period of quiet."