Fatah, the faction that had dominated the legislative council until it was beaten by Hamas in January elections, boycotted the parliamentary vote having earlier walked out of the chamber in protest.
Hamas now controls the 132-member Palestinian Legislative Council with 74 seats, compared with 45 for Fatah.
The absence of the Fatah MPs meant that while 64 MPs voted to repeal the measures, there were no votes against and only six abstentions.
On February 13, the outgoing parliament appointed Fatah members to key administrative posts and backed the creation of a constitutional court, whose members would be named by Mr Abbas.
Deputies from Hamas believe that because the session was held after the election in which Fatah was defeated, its decisions were invalid.
Upon taking up his post last month, new Hamas speaker Aziz Dweik immediately froze those decisions and said they would be reviewed by the new house.
In a statement after the vote the Fatah MPs denounced what they called "the violations of the law which have been committed during this session and the manner in which proceedings have been handled" by Mr Dweik.
Hamas prime minister-designate Ismail Haniya has been formally asked by Mr Abbas to form a new government, which is likely to be agreed by the end of the month.
Hamas leader vows arms
The leader of Hamas, Khaled Meshaal, has vowed to continue armed struggle against Israel and declared that the Palestinian Authority had accomplished nothing by recognising the Jewish state.
"The demand that Hamas and the resistance movements lay down their weapons and become political parties is unrealistic and has nothing to do with the Palestinian reality on the ground," he said in an interview on Arab news channel Al-Arabiya.
"This is why we are determined to hold on to our choices which are resisting and defending our people with the modest arms that we have while opting for peaceful politics to reorganise the internal Palestinian order."
Mr Meshaal made clear his group, which has carried out dozens of attacks against Israel, had no plans to compromise its militancy.
He reiterated Hamas demands including Israel's return to the pre-1967 borders and the repatriation of Palestinian refugees.
The parties trying to broker the roadmap peace deal, the so-called Middle East Quartet grouping the European Union, Russia, the United Nations and the US, say Hamas must renounce violence and recognise Israel's right to exist.
Mr Meshaal, who was also interviewed by Al-Jazeera television, said the roadmap died last summer when the US administration agreed to Israel's unilateral pullout from the Gaza Strip.
He warned that Acting Israeli Prime Minister Ehud Olmert was set to repeat the feat in the West Bank.
Kadima split over pullouts
Mr Olmert, who has pledged not to have any dealings with a Hamas-led government, says if his Kadima party wins the March 28 general election, Israel will carry out more unilateral withdrawals in the West Bank.
But there were major divisions within Kadima over the plans for a new round of unilateral pullouts.
One of the party's top candidates, former security service chief Avi Dichter, said Kadima would immediately start working on a new "disengagement" if it won the election.
But dovish former premier Shimon Peres, second on Kadima's list of candidates after Mr Olmert, said the government would be better off trying to negotiate with the Palestinians within the framework of the roadmap peace plan rather than go it alone.
Education Minister Meir Sheetrit also said Kadima should remain committed to the roadmap, which targets the creation of a Palestinian state alongside a secure Israel.
Mr Olmert has already indicated he will make fixing the final borders of the Jewish state his top priority after the election which polls show should be won by his Kadima party.
Gaza air strike
Meanwhile, three Palestinian children and two members of the hardline Islamic Jihad movement were killed on Monday in an Israeli air strike in Gaza City.
The two Jihad activists were travelling in a car in central Gaza City when it exploded into a ball of flames after an Israeli aircraft fired at least one missile into the vehicle.
An eight-year-old boy and a teenager were also killed in the massive explosion. Another teenage boy died later from his wounds.
An Israeli army spokeswoman confirmed that the military carried out an air strike targeting a militant from Islamic Jihad wanted in connection with rocket attacks on Israel.
While its larger rival Hamas halted its campaign of anti-Israeli attacks in the past year, Jihad has carried out half a dozen suicide bombings inside Israel.