Talabani rejected an earlier version of the law after it was passed at parliamentary session in July, which had been boycotted by Kurdish parties and some Shia MPs.
Salim al-Jubouri, a senior member from the Sunni Arab Accordance Front, said the law had been passed unanimously after a number of concessions were made over the Kirkuk issue.
He said there would be a separate law for dealing with elections in Kirkuk as well as a power sharing formula for the city's administration.
Kurdish politicans had objected to a power-sharing arrangement for the oil-rich area, which they want to incorporate into their autonomous region in the north.
On Wednesday, Kurdish, Shia, Sunni and Turkomen politicians agreed to form a parliamentary committee to review disputes regarding Kirkuk and report to the
house by March 2009.
Mahmoud al-Mashhadani, the parliamentary speaker, and the electoral commission had been urging a speedy resolution of the impasse over the elections law to enable a vote to take place before the end of the year.
The polls were scheduled to take place on October 1, but on Wednesday they set a deadline of January 1, 2009 for the vote.
Washinton had been pushing Iraq to reach a compromise so that the local elections, which it believes will help reconcile rival ethnic groups, be held.