Palestinian factions will "start soon an intra-national dialogue regarding the formation of a unity government that will bear its responsibilities in the coming stage", Xinhua news agency quoted the spokesman as saying in a statement.
The announcement came after Abbas issued a decree to postpone the general elections in the Palestinian territories, prompting backlashes against the President from other factions.
On April 30, Abbas announced in a televised speech that the 2021 general elections scheduled for May 22 were postponed until further notice and "until the participation of our people in East Jerusalem is guaranteed".
Azzam al-Ahmad, member of the Palestine Liberation Organization (PLO)'s executive committee, told state radio Voice of Palestine on Saturday that the leadership "will be ready to set up a new date for holding the elections, if Israel agrees to hold them in East Jerusalem".
Al-Ahmad called on the international community "to play a positive role toward holding the Palestinian elections by exerting pressure on Israel to abide by the agreements it signed with the Palestinians".
The issue of East Jerusalem, which was occupied by Israel in 1967, is one of the most sensitive issues for the Palestinians, who wanted it to be the capital of their future independent Palestinian state.
Israel does not allow the Palestinian Authority to carry out political activities in the city.
However, according to the Oslo peace accords signed with Israel, the Palestinians in East Jerusalem are allowed to vote at the Israeli post offices in the city.
In January, Abbas announced the 2021 general elections will include the legislative elections on May 22, the presidential elections on July 31, and the elections of the Palestinian National Council, the highest decision-making body of the PLO, on August 31.