BAGHDAD -- Iraq's bickering politicians finally agreed on a new election law yesterday, paving the way for crucial national elections to take place in January and for the drawdown of U.S. troops to proceed as scheduled.

Parliament's passage of the law came so late that the election now cannot be held as had been planned on Jan. 16, said U.S. Ambassador Christopher Hill, and would likely be moved to Jan. 23. But that is well within the end of January deadline mandated by Iraq's constitution, and he said the short delay would make no difference to the U.S. military's plans to bring all combat troops home by the end of August.

"What is significant about the date ... in January is that the troops can be drawn down on schedule," Mr. Hill told reporters in a conference call after the vote in Iraq's parliament. "We can achieve the January time frame and the responsible drawdown as expected."

The protracted deadlock over the new law had raised concerns about the stability of Iraq's fledgling democracy and the ability of Iraqi politicians to resolve the many unresolved issues that may still confront them once U.S. combat troops have gone, including the thorny issue of the contested oil-rich province of Kirkuk, which proved the biggest obstacle to the new law.

In Washington, President Barack Obama hailed the agreement as "an important milestone" for Iraq.

"This agreement advances the political progress that can bring lasting peace and unity to Iraq, and allow for the orderly and responsible transition of American combat troops out of Iraq by next September," he said at the White House.

U.S. commanders have linked the pullout to the election because they want to be sure Iraq is stable before the troops start to leave in significant numbers. Gen. Ray Odierno, the overall commander, is to make an assessment of security conditions 60 days after the poll before giving the final word on whether the withdrawal will go ahead under the planned timetable. A residual force of 50,000 is due to remain behind until the end of 2011 to train Iraqi troops and provide logistical support.

The election law was passed by 145 out of the 196 lawmakers present. The vote came at the end of another intensive day of negotiations, during which the U.S. ambassador was seen striding through the hallways, flanked by diplomats, as he circulated among the factions to press them to reach an agreement.

Though the U.S. ceded the lead role in the negotiations to the United Nations, American diplomats stepped up their involvement in the talks as the stalemate dragged on. But Mr. Hill credited the Iraqis with coming up with the solutions that sealed the deal. "This is really a made-in-Iraq election law," he said.

The biggest snag concerned the issue of how voting would proceed in Kirkuk, whose population has been swelled in recent years by an influx of Kurds claiming to be reversing the policy of Arabization undertaken by Saddam Hussein.

Arabs and Turkmens allege the Kurdish immigration has far exceeded the numbers expelled by Hussein, as Kurds seek to boost their claims to ownership of the province. In the end, the factions came up with a compromise formula under which all registered voters in Kirkuk will be eligible to vote, but a special committee will spend the year after the election reviewing voter rolls in Kirkuk and other "suspect" provinces to see whether there are irregularities. Kurds claim other provinces, including Nineveh and Baghdad, also have seen a suspiciously large growth in the number of registered voters since the last election.

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