The Israeli cabinet has ruled that Palestinian residents of occupied East Jerusalem can vote in Palestinian elections on 25 January.
Israel has softened its curbs on campaigning in East Jerusalem
Israel had threatened to ban voting there, and is still refusing to allow militant group Hamas to take part.
Hamas said it would find other ways of campaigning and joining the ballot.
Palestinian leader Mahmoud Abbas said he would delay the poll if a vote was barred, and had Washington's support for the ballot to go ahead as planned.
Correspondents say Israel does not want to be responsible for a cancellation.
The BBC's Richard Galpin in Jerusalem says the decision is one of the most important taken by the government since Prime Minister Ariel Sharon suffered a severe stroke on 4 January.
Tests have shown activity on both sides of his brain, but he shows no sign of emerging from a medically induced coma.
His replacement, Ehud Olmert, is set to stay on as acting prime minister until Israel goes to the polls on 28 March, according to Israeli media.
Attorney General Meni Mazuz will reportedly tell Mr Olmert on Sunday that he can continue in his current capacity, because Mr Sharon remains unable to run the country.
The cabinet's final decision to allow voting comes after both Israeli Defence Minister Shaul Mofaz and Mr Olmert had said it would go ahead.
Scheduled for 25 January; originally set for July 2005
132 members elected to Palestinian Legislative Council (PLC)
Fatah and Hamas are main contenders
First time Hamas participates in parliamentary poll
Last parliamentary elections held in 1996
But the government has decided to ban Hamas from campaigning and to block its inclusion on ballot papers distributed in the area.
Palestinian negotiator Saeb Erekat welcomed the approval, but both he and a Hamas spokesman condemned the conditions attached.
"Hamas and other factions are able to carry out their election campaign in many ways and in different methods despite the Zionist blackmail," Mushir al-Masri said.
Our correspondent says Israel does not want to help the Islamist militant group come to power, as it has carried out many suicide bombings and calls for the destruction of the Jewish state.
Polls suggest the organisation could win up to a third of the Palestinian vote in the election, which it is competing in for the first time.
But Israel does not want to be held responsible for scuppering the Palestinians' first parliamentary poll in 10 years, our correspondent adds.
Israel had already softened its initial curbs on campaigning in East Jerusalem, to allow canvassing in the area.
Israel has occupied East Jerusalem since 1967. It has annexed the area and sees it as its exclusive domain.
Under international law the area is considered to be occupied territory.
The area is often called Arab East Jerusalem because the majority of its residents are Palestinian, and Palestinians hope to make it their future capital.
The 200,000-odd Palestinians living in the eastern part of East Jerusalem were allowed to vote in an election in 1996, in which Hamas did not take part.