Defence Minister Shaul Mofaz announced that Israel had agreed in principle to allow Palestinians in the Arab quarter of the holy city, occupied and annexed by the Jewish state since 1967, to vote in the landmark polls.
The move comes after Israel, angered by the participation of Islamist group Hamas, which has been behind a majority of deadly anti-Israeli attacks in the last five years, had initially said it would ban voting in east Jerusalem.
US assurances
Mr Abbas said he had received assurances from the United States that Israel would allow the polls to take place in keeping with the same arrangements during the only previous Palestinian parliamentary election in 1996.
"Today I received American assurances that the elections as well as electoral campaigning will take place in Jerusalem in keeping with the arrangements in 1996," Mr Abbas told a news conference in Gaza City.
"As a result the elections will take place on the scheduled date," he said.
The head of the central elections committee, Ammar Dweik, said that the Israelis telephoned the director of the commission in Jerusalem on Monday evening to inform him the election could take place in the city as in 1996.
"They told him that they would allow the election campaign (as well as voting) to take place in Jerusalem, according to the agreement that was signed in 1996," Mr Dweik said.
At the only previous Palestinian parliamentary election in 1996, Israel authorised Arabs living in east Jerusalem to vote at post offices, as was also the case for a presidential ballot in 2005.
Mr Abbas had threatened to cancel the whole election on January 25 if Israel did not allow voting in the east of the holy city.
The Palestinian leader, whose ruling Fatah party faces a huge challenge from Hamas in the elections, said he had instructed security services to ensure that "protect the day of democracy even by force".
He exhorted candidates or voters not to carry arms on that day, with the Palestinian Authority seemingly increasingly powerless to clampdown on armed chaos in parts of the Gaza Strip and West Bank.
"We have agreed in principle that the same rules which were applied in the previous elections will also apply this time," Mofaz said on public television.
Green light
Public Security Minister Gideon Ezra earlier gave the green light for parliamentary candidates, except those from Hamas, to campaign in the city.
Mr Ezra said candidates would be able to canvass in east Jerusalem, but only with permission and ruled out authorisation for anyone from the Hamas.
In Jerusalem's walled Old City, many local residents, more interested in shopping for the Muslim Feast of the Sacrifice, were seemingly indifferent to the prospect of an election that they believed would change little.
"I don't like the elections. The candidates do nothing for the Palestinians. Abbas just goes abroad all the time," said Mohammed Mahmud, an unemployed 38-year-old father of 10 who doubted he would bother to vote.
Hatem Abdelkader, the ruling Fatah faction's main candidate in the city, said he had been cleared to campaign provided police are informed of electoral meetings and posters are erected only on billboards.
Two prominent candidates, independent MP Hanan Ashrawi and presidential election runner-up Mustafa Barghuti, were last week forcibly stopped while canvassing in the Arab quarter of the Old City.
"We reject the conditions imposed such as getting police permission or excluding candidates from Hamas," Ashrawi said.
Hamas crowed that Israel had backpedaled from a previous ban on all Palestinian electoral activity in east Jerusalem.
"This decision is a climbdown in the Israeli position," spokesman Sami Abu Zuhri said.
"They are trying to interfere in Hamas's electoral campaign but we are capable of reaching out to our audience in various ways."