Majed Abu Shammala, a Fatah MP, said both sides hoped to end internal violence that has killed nearly 20 people in Gaza in the past month.
Mahmoud Abbas, the Fatah leader and Palestinian president, has given the Hamas government until the end of the week to accept a manifesto calling for a Palestinian state that implicitly recognises Israel - or the issue will be put to the people.
His spokesman said on Wednesday that Abbas will issue a decree on Saturday setting the stage for the referendum if the Islamist group still refuses to back the proposal.
"President Abbas will issue the decree on Saturday," Nabil Abu Rudeina told reporters in Ramallah in the West Bank.
Many Palestinians fear that a referendum could trigger more violence between the rival factions.
Fatah and Hamas leaders urged calm on Wednesday after a meeting brokered by Egyptian officials in the Gaza Strip.
"We order men from Fatah and Hamas to respect the holiness of Palestinian blood," said Khalil Al-Hayya, a Hamas leader.
"We order men from Fatah and Hamas to respect the holiness of Palestinian blood"
Khalil Al-Hayya, a Hamas leader
Previous agreements to end factional bloodshed were short-lived.
Fatah, which lost a general election to Hamas in January after 12 years at the helm, has had difficulties accepting defeat.
The Palestinian flagship movement founded and headed by the late Yasser Arafat until his death in 2004, supports a negotiated peace with Israel.
Hamas does not recognise Israel and Western powers have responded to its government's stance with stringent aid cuts.
The two factions have also clashed over control of the unwieldy Palestinian security apparatus.
Angered by some of the president's security appointments, Hamas set up its own security group last month even though Abbas had banned the force.
Moreover, the Islamists reject the statehood manifesto written by prisoners held in Israeli jails and say a referendum would be irrelevant so soon after elections.
Civilians duck during clashes
between Fatah and Hamas
Abbas, a moderate who was elected president early last year in a ballot Hamas did not contest, had set a deadline of Tuesday for the Islamists to accept the manifesto, but held off after what officials said were appeals by Arab leaders.
A referendum would be seen as a confidence vote on the Hamas. Opinion polls show that most Palestinians support the manifesto.
The document calls for a Palestinian state on all of the West Bank and Gaza Strip, which Israel captured in the 1967 Middle East war.
Israel has long insisted on keeping large Jewish settlement blocs in the occupied West Bank - a plan that has received the blessing of the US president.
Hamas has previously proposed a long-term truce if Israel gives up the West Bank and east Jerusalem, far short of meeting the demands of Israel or Western countries.
The Hamas prime minister, Ismail Haniya, urged Abbas on Wednesday to be open to further discussions on the prisoners' document.
"The battle with the Israeli occupation is tough and long and we should not be dragged into side battles"
He also reiterated that Palestinians should avoid civil war.
"The battle with the Israeli occupation is tough and long and we should not be dragged into side battles," Haniya said.