"Unfortunately we have lost time for January 16. We have sent a letter to parliament telling them we have lost that date," he told Al Jazeera.
"Still there is an opportunity to have the election in time, according to the constitution ... by the 31st of January.
"We need at least seven days more to have the election and this will be under the authority of the presidency council ... which will issue the order to announce the day of the election."
The election law provides for an open candidate list, allowing voters to cast their ballot for an individual rather than a party. It also sets aside five seats in parliament for minorities.
The dispute over Kirkuk revolved around voter registration lists.
MPs voted into law the Kurdish proposal that current lists be used in next year's polls and that Kirkuk be kept as one electoral constituency.
A number of Arab and Turkmen politicians, who wanted the 2004 or 2005 records to be used and Kirkuk to be split into two constituencies, boycotted Sunday's vote.
Mosab Jasim, Al Jazeera's Iraq producer, said: "The compromise in the case of Kirkuk is that elections in Kirkuk will be held alongside those in the rest of Iraq's provinces.
"There is no special date for Kirkuk, there is no special treatment for Kirkuk except that if there is any claim of fraud, there is a special committee to investigate," he said.
"If the fraud if proved, then the elections in Kirkuk can be cancelled and rerun in one year."
Ethnic Kurds claim that Kirkuk, which sits on vast oil resources, is part of their ancestral homeland and want it included in their semi-autonomous northern region.
But the province is also home to a large number of Arabs and Turkmen who fiercely oppose Kurdish efforts to take it out of the control of the federal government.
Alaa Makki, a Sunni member of parliament from the Iraqi Islamic Party in Baghdad, said: "I think this law is the most important law in Iraq passed by the parliament since its establishment in 2006 because it could maintain the political process from being disturbed.
"Every partner - the Kurd, the Arab, the Turkman - accepted to pass this law by simple voting and we regard this is as a success for the coming challenges for Iraqis, he said.
Makki said: "The law maintains all the rights of all of Iraq's political partners".
Mahmoud Othman, a Kurdish member of the Iraqi parliament, told Al Jazeera that the passing of the election law would be welcomed in Kirkuk.
"It was a good occasion. We are happy. We agreed and voted on the law and it's passed now. The election will be on time," he said.
"People will be happy about it in Kirkuk."
During the day-long session, Christopher Hill, the US ambassador to Iraq, could be seen shuttling between various political factions.
"We congratulate members of the Council of Representatives for coming to agreement on the various difficult issues of considerable importance to Iraqis," Hill and General Ray Odierno, the highest-ranking US military official in Iraq, said in a statement.
"With the passage of this law, the Iraqi people, through their representatives, have shown their desire to uphold democratic and consultative government."
Barack Obama, the US president, said that the approval of the law paved the way for the withdrawal of US forces from the country.
"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.
The parliamentary election is seen as a crucial test for the country as it attempts to emerge from the sectarian carnage and civil strife that has followed the US-led invasion in 2003.