Baghdad, Iraq (CNN) -- The fate of Iraq's newly revised election law again hinges on the approval of the country's Sunni Arab vice president, who is under pressure to sign the much-contested plan.
The new bill has been approved by the other two members of the presidency council. Adel Abdul Mahdi, the country's Shiite vice president, issued a statement Thursday saying he and President Jalal Talabani, who is Kurdish, have put their signatures on it.
But Tariq al-Hashimi, the country's Sunni Arab vice president, who vetoed the original election bill last week, continues to threaten to veto this revised measure, and Mahdi and Talabani are trying to persuade him to sign the document.
Al-Hashimi's vote is key because in Iraq, legislation passed by the parliament must be ratified unanimously by the presidency council, made up of the country's two vice presidents and the president.
"All the efforts are devoted to have the entire presidency council approval on the the law, coming from the joint concern about elections to take place in the specified date," Mahdi said in a statement.
But al-Hashimi said Wednesday that the "veto is still an option and it will be used if I find that the current law doesn't conform to the [Iraqi] justice and the constitution."
The upcoming parliamentary elections and a law setting down rules for elections are seen as important barometers of Iraqi progress toward stability.
The election is also key step in plans for a U.S. withdrawal from Iraq, About 115,000 American troops remain in Iraq, and the Obama administration plans to pull all but 30,000 to 50,000 of them out of the country by August.
Al-Hashimi vetoed the Iraqi parliament's first election law last week, arguing it failed to provide enough seats for Iraqi refugees, many of whom are Sunnis.
A revised bill passed by Iraq's parliament on Monday remains "unconstitutional and unfair," al-Hashimi said in a statement issued by his office.
The previous law "was more fair to Iraqis than the new law, which Mr. al-Hashimi will deal with just like he dealt with the previous one," the statement said. Iraq's constitution calls for elections by January 31.
Disputes over how seats will be allocated in a new parliament have put the vote in jeopardy.
Lawmakers need a two-thirds majority to override a veto, but Iraq's parliament adjourned until December 8 after passing Monday's revised bill.
Iraq's top electoral commission -- saying it needs 60 days to prepare for voting -- announced last week that a January vote is unlikely.
Al-Hashimi said the election bill is unfair to Iraqis who were forced to flee violence in their homeland, and he refused to sign it without an amendment that would increase the number of seats allocated to refugees and small political parties that could not get enough votes on a national level.
In addition to al-Hashimi's objections, Kurdish leaders had threatened to boycott the upcoming vote unless provinces with heavy Kurdish populations get greater representation in the next parliament.
The law that parliament passed Monday included revisions the Kurds had sought, but not those al-Hashimi demanded.
Al-Hashimi's office said the new law was passed without "national accordance" and outside parliament's usual way to deal with "sensitive national legislation of this caliber."
"What happened constitutes a dangerous precedent that will negatively overshadow the overall political process," the statement said.
Asked whether the political holdups in passing a law will mean a delay in the election and troop withdrawals, U.S. Gen. Ray Odierno told CNN Thursday that the withdrawal schedule is not as important as getting a law.
"Their democratic process is working, and I think it's important that they have a law that everyone will accept so we can move forward together -- that's the most important thing. I believe we have enough flexibility we'll be able to mitigate it and we'll be able to go on and have successful elections," said Odierno, the top U.S. commander in Iraq.