"Hamas has no problem in attending [such a meeting] and we were the first to call for Palestinian-Palestinian talks to end the internal conflict," Barhoum said.
The two main Palestinian movements have been bitterly divided since Hamas seized full control of the Gaza Strip in June 2007, pushing out security forces loyal to Mahmoud Abbas, the Palestinian president and Fatah leader.
Dr Abdallah Abdallah, a member of the Palestinian parliament for Fatah, told Al Jazeera: "The Egyptian government has submitted its invitation to all thirteen Palestinian factions."
He did not confirm if Fatah would attend the talks.
Usamah Hamdan, a senior Hamas official, told Al Jazeera: "Abu Mazen [Abbas] does not intend to attend direct talks with Hamas and Fatah, or the meeting being held with all the Palestinian factions.
"But some members of Hamas will attend this meeting. This draft needs a lot of work to be a good proposal for the Palestinians. It shows that Fatah has a very negative position which will not help the Palestinians reunite themselves," he said.
Presidential term
The divisions between Fatah and Hamas have grown worse in recent weeks amid a disagreement over when Abbas's presidential term ends.
Hamas has said that Abbas, elected in January 2005, will cease to be president once his constitutionally mandated four-year term officially expires on January 8.
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"All factions have agreed that the Palestinian Liberation Organisation ... will be solely responsible for negotiations with Israel"
Nour Odeh, Al Jazeera correspondent in Ramallah
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Abbas loyalists, citing a Palestinian law, say that presidential and parliamentary elections must be held at the same time, which would extend his term to 2010.
"The Egyptian government has submitted its invitation to all thirteen Palestinian factions," Dr Abdallah Abdallah, a member of the Palestinian parliament for Fatah, told Al Jazeera.
Abbas has called for the establishment of a politically independent national unity government to pave the way for elections to be held at an agreed upon time.
This position was reflected in a draft reconciliation plan, obtained by Al Jazeera, that has been put forward by Egyptian mediators ahead of the talks.
The plan calls for "the establishment of a national consensus government" that would lift the international blockade of the Hamas-ruled Gaza Strip and prepare for presidential and parliamentary elections.
Israel imposed a blockade on the Gaza Strip after Hamas took full control, limiting supplies and economic activity in the territory.
The plan also also provides for an independent Palestinian security force with assistance from Arab states and the incorporation of Hamas into the Palestine Liberation Organisation (PLO) headed by Abbas, which is responsible for negotiations with Israel.
Reconciliation 'roadmap'
"Basically what the draft entails is a declaration of principles that Egypt wants all Palestinian factions, not just Hamas and Fatah to sign on to this deal ... [and] agree to be part of committees that will discuss each point that all factions have agreed on," Al Jazeera's Nour Odeh, reporting from the West Bank city of Ramallah, said.
The draft is seen as a "roadmap to reaching national reconciliation for Palestinians and they have outlined them in the number of points which we have already heard from Fatah and Hamas and other factions that they agree on," she said.
"But the devil is in the details and we will wait to see how far these factions will go in reaching a consensus on each of those points.
"All factions have agreed that Palestine Liberation Organisation (PLO) headed by president Mahmoud Abbas at the moment, will be the party solely responsible for negotiations with Israel," she said.
Israel, the European Union and United States consider Hamas to be a "terrorist" organisation and concerns have been raised that full reconciliation could lead to sanctions.