Here are answers to some questions about how the government will be formed:
What happens at Saturday's parliament session?
Abbas will give a speech asking the new government to respect the Palestinian Authority's commitments and agreements.
But he is not expected to demand that Hamas recognise Israel and renounce violence as a precondition to forming the government.
Hamas rejects Israel's right to exist and has spearheaded an armed resistance campaign.
Hamas will present its own political programme which may not be in harmony with Abbas's commitment to peacemaking, setting the stage for confrontation between the cabinet and president.
How will the new prime minister be chosen?
After the parliament session, Abbas will ask Hamas to name its prime minister.
Abbas will ask him to form a government.
Ismail Haniyah is tipped to take
the job as premier
Hamas leader Ismail Haniyah from the Gaza Strip is tipped to take the job.
Deputies will also elect the Palestinian Legislative Council's speaker.
The likely candidate will be Hamas's choice Aziz Dweik.
How long will it take to form a government?
According to the law, Hamas has three weeks to form a government with a two-week extension if required.
If Hamas fails to form a government during this period, Abbas has the right to ask another parliamentary bloc or anybody from outside parliament to form a government.
Hamas has said its government will be ready by early March.
Who will join the government?
Hamas still hopes to convince Fatah, now the largest opposition group, to join its government.
Fatah has refused.
Some Hamas officials say they prefer a national coalition cabinet with other factions and independents, but others say they might appoint only Hamas ministers.
Their final decision will be made after Fatah's leadership meets next week.
How will the world deal with a Hamas-led government?
Israel and the United States have already said they will not deal with a Palestinian administration run by Hamas, which appears on US and European Union lists of terrorist groups.
The European Union, the biggest donor, has said it will suspend direct aid to the cash-strapped Palestinian Authority unless Hamas renounces violence and recognises Israel.
Hamas's first challenge will be dealing with cuts to foreign aid as well as the freezing of some $500 million in taxes transferred by Israel annually to the Palestinian Authority.
Who is Hamas?
Hamas means zeal and is an acronym for Harakat al-Muqawamah al-Islamiyyah (Islamic Resistance Movement).
Formed in 1987 at the beginning of the first intifada against Israel's occupation of the West Bank and Gaza, Hamas is the largest Palestinian resistance movement.
Hamas says Palestinian land
should not be given up
The movement is an offshoot of the Muslim Brotherhood (Ikhwanul Muslimeen).
Hamas enjoys wide support among Palestinians, mainly in the Gaza Strip and West Bank.
The movement has a social-welfare and military wing, but is perhaps better known in the West for the latter.
Its social-welfare activities include the running of schools, clinics and welfare programmes.
Hamas' military wing has engaged in armed resistance to Israeli occupation including attacks on Israeli targets and Israel.
Israel often targets the movement's leaders for assassination. One of the movement's founders and spiritual leader, Shaikh Ahmad Yasin was killed in a missile attack on 22 March 2004, after an unsuccessful attempt on his life six months before.
Abd al-Aziz al-Rantisi, who became leader after Yasin's killing, too was assassinated by Israel on 17 April 2004.
Hamas, according to its manifesto, believes that "the land of Palestine is an Islamic Waqf (trust) consecrated for future Muslim generations... It, or any part of it, should not be squandered: it, or any part of it, should not be given up".