Quraya has been holding talks with members of the Higher Follow-up Committee for Intifada (HFCI), Aljazeera's correspondent in Gaza reports.
Sunday's meeting was the second in less than 24 hours.
AFP reports that the talks in Gaza City were part of efforts to reach an agreement for a halt to anti-Israeli attacks.
Political representatives of groups such as Islamic Jihad, the Popular Front for the Liberation of Palestine (PFLP) and the Democratic Front for the Liberation of Palestine (DFLP) took part in the meeting of the HFCI with Quraya.
However, the main Islamic resistance movement Hamas was not present, with members saying that organisers had not been able to contact them in time.
"We discussed the prospects for a mutual ceasefire which would see an end to the Israeli violations against us," Quraya said after the meeting.
"We also talked about our (Palestinian Authority) contacts with the Israelis and how best to present our case."
Palestinian Authority President Mahmud Abbas has persuaded the factions to observe a temporary cooling down period but wants Israel to match any formal ceasefire declaration by ending its military operations in the occupied territories and starting to release Palestinian prisoners.
With deployment of police, there
has been a downturn in violence
Nafaz Azzam, a local leader of Islamic Jihad, said the meeting took place in a positive atmosphere.
"We talked about a ceasefire, but everybody, including Abu Ala [Quraya], agreed that this ceasefire should be not just be from one side and not for free," he said.
"The Palestinian people need genuine measures from Israel on the ground."
Amid a general downturn in violence and with Palestinian security forces on patrol in Gaza, Israel has agreed to halt offensive operations in the territory.
It still retains security control in the larger West Bank, but is expected to transfer responsibility to the PA in at least four towns this week.
Earlier, a Palestinian was shot dead by Israeli occupation troops manning the Rafah border crossing between Egypt and the southern Gaza Strip, medical and military sources said.
The victim was identified by Palestinian sources on Sunday as Eid Abu Rubaiha, 55.
His body was handed over to Palestinian authorities after he was shot in a closed military zone about 15m from an Israeli army-manned border post, military sources said.
The latest deaths raised to 4724 the number of people killed since the start of the Palestinian intifada, or uprising, in September 2000, including 3669 Palestinians and 981 Israelis.