BAGHDAD, Iraq (CNN) -- Iraqi lawmakers are close to an agreement over the country's controversial elections, and they hope to vote on the legislation Saturday, the parliament said on its Web site.

Passage of the law by the 275-member Council of Representatives two days from now would ensure that national elections would be held on the scheduled date of January 16.

Parliament's speaker, Ayad al-Samarraie, said the nation's three-member presidency council -- composed of the president and the two vice presidents -- were meeting with political party leaders to forge an accord, according to the Web site.

Iraq's Independent High Electoral Commission has said it needs at least 90 days after passage of any election law to prepare to carry out the voting, which U.S. and Iraqi government officials call a vital step in Iraqi efforts to solidify a democratic system in the post-Saddam Hussein era.

But there had been a lack of clarity over what the deadline would be for avoiding a delay in the vote.

The election commission's chief, Judge Qassim Aboodi, told CNN that Thursday is D-Day for the new law, which will specify how the January 16 election will be carried out. Any further delays would not provide enough time for ballots, which are being printed abroad, to arrive in Iraq, he said.

But Iraqi lawmakers, such as Mahmoud Othman, said that despite the electoral commission deadline of the end of the day Thursday, a vote in two or three days will not delay the election.

The ballots will be printed according to what parliament chooses: open lists that name candidates or closed lists that name only the parties. The law used in the 2005 election calls for a closed list. The question of which list to use has been one of the issues holding up the passage of the legislation.

But the biggest roadblock to a new election law is the question of how balloting should unfold in the ethnically diverse oil-rich province of Kirkuk, where Kurds displaced under Saddam Hussein's rule have returned to claim back their land.

The power struggle among Kurds, Arabs and Turkmens has been a political hot potato.

Kurds have long regarded Kirkuk -- the province and the city of the same name -- as an integral part of Kurdistan and many want it to be part of Iraq's autonomous Kurdish region. Arabs and Turkmen also lay claim to the city and province, and all the groups want their voices and votes to be adequately represented in the political system.

Disgruntled Arab and Turkmen residents say many more Kurds have moved into Kirkuk than were displaced, and that allowing them to vote would create an unfair advantage. Arabs and Turkmens want special measures to adjust for the increased numbers because they believe many of the Kurdish immigrants are there illegally. The Kurds insist there should be no special voting procedures, and reject a United Nations' proposal that singles out Kirkuk for special treatment.

The disagreements among the groups spurred the postponement of provincial elections in Kirkuk last January because officials there could not agree on how to apportion seats among the ethnic groups.

Othman, a Kurdish representative, said Monday that the United States is pressuring the "highest levels of the Kurdish leadership" to accept a compromise that would dictate how national elections would be held in January.

U.S. Vice President Joe Biden broached the issue of elections in telephone calls Sunday with Iraqi Kurdistan President Massoud Barzani and parliamentary Speaker al-Samarraie, said Biden spokesman Jay Carney.

"In both calls, the vice president echoed the president's position that timely elections are important and that we urge all parties to do their part to make them happen," he said.

A secure environment and political stability during and after the polls will be key as the United States looks to withdraw combat troops by next August, leaving 50,000 personnel in advisory roles until they, too, are withdrawn by the end of 2011.