The Palestinian parliament has voted overwhelmingly to create a new post of prime minister, in what is seen as a significant reform move.
Mr Arafat and Mr Abbas have reportedly agreed on the division of power
The Palestinian leader, Yasser Arafat, finally agreed last month to loosen his grip on power after persistent international pressure.
He has nominated his deputy, Mahmoud Abbas, to be the first prime minister.
Monday's meeting in the West Bank town of Ramallah was called to decide on the appointment and powers of the prime minister.
It is thought that Mr Arafat will remain in control of two key issues - security and peace talks with Israel.
The new prime minister will deal mainly with internal affairs - including naming and supervising cabinet ministers.
Mr Arafat appears to be able to appoint and dismiss the premier.
Changes at the top
The Palestinian leader has thrown his weight behind the reform process.
He also said he was prepared to resume security coordination with Israel, called again on all Palestinian factions to observe a ceasefire and re-affirmed his commitment to peace based on a two-state solution.
NEW PALESTINIAN POWER-SHARING ARRANGEMENT
Mr Arafat controls security and foreign policy - including peace talks
Mr Arafat has right to appoint and dismiss premier
Prime minister will be in charge of internal affairs and forming a government
Mr Arafat and Mr Abbas - also known as Abu Mazen - are reported to have agreed on the division of power.
The BBC's Barbara Plett in Ramallah says the new plan would probably satisfy most Palestinians who have been demanding better government, not a change in leader.
But she says it is not clear whether such an arrangement would satisfy Israel and the US.
The Israelis want the Palestinian leader to take a largely ceremonial role.
US President George Bush has for his part said the Palestinians need to choose new leaders as a precondition for statehood.
Mr Abbas has said he will decide on whether he wants the job once parliament decides what powers he will have.
Officials said the meeting of the Palestinian Legislative Council is expected to last into Tuesday.
At the weekend, the Palestine Liberation Organisation - which represents Palestinians at home and abroad - approved Mr Abbas' nomination.
On Monday, deputies of the 88-member parliament voted 64-3 with four abstentions in favour of a prime minister.
Seventy-eight of them are present in Mr Arafat's compound in Ramallah for the session, while 10 others are participating via video conference from Gaza, after being barred by Israel from travelling to the West Bank, the Associated Press news agency said.
Mr Arafat has been the unchallenged leader of his movement since the late 1960s and remains widely popular.
Correspondents say that although Mr Abbas, 68, lacks the charisma and high media profile of the Palestinian leader, he has often been mentioned as a potential successor to Mr Arafat.
He is secretary-general of the PLO executive and a co-founder of the Fatah movement.
Concerns have previously been raised over Mr Abbas' health, but he remains a figure who would be acceptable to most Palestinians.