BAGHDAD - A long-sought political consensus in Iraq over how to conduct crucial upcoming elections fell apart Tuesday over the thorny issue of the oil-rich city of Kirkuk, an Iraqi lawmaker said.

The new snag came as an al Qaeda-linked group claimed responsibility for the twin suicide bombings in the heart of Baghdad Sunday that killed at least 155 people.

Many fear the political deadlock over the new law will delay elections, now slated for January, and open the door to renewed violence in Iraq after it stepped back from the brink of civil war two years ago.

Mahmoud Othman, a Kurdish lawmaker, told The Associated Press that an emergency proposal by the nation's leaders to break the deadlock over the election law had fallen apart over the fractious northern city split between Arabs and Kurds.

Othman said the vote over the election law would not take place Tuesday. There was no information about when the matter would be addressed.

Just one day after the massive security failure in the capital, there appeared to be quick progress on the election law. With Iraq's public already angry over the bombing and the resurgence of violence, the politicians appeared to not want to risk further angering people by delaying the elections with their internal wrangling.

On Monday night, Iraqi Prime Minister Nouri al-Maliki and others agreed on a compromise over voting in Kirkuk as the Shiite-dominated government pushed to smooth over differences in the divided parliament and wrap up the law so elections could proceed on time.

In Kirkuk, which is claimed by Kurds, Arabs and Turkomens, the dispute focuses on whether all the people living there should be allowed to vote in the election.

During the Saddam era, tens of thousands of Kurds were displaced under a forced plan to make Kirkuk predominantly Arab. Since the 2003 U.S.-led invasion of Iraq, many of these Kurds have returned. Now other groups claim there are more Kurds than before -- which could sway the vote in their favour and bring Kirkuk and its oil fully under Kurdish control.

Arabs and Turkomen would like the city to be divided into four districts in which they would have some plurality, while the Kurds want the whole city to be a single district that they could dominate with their swelling numbers.

There is also a dispute about how to count voters. Arabs favour a plan that would use the 2004 voter registry, likely meaning Arab voters would be much more represented than Kurds.

The Kurds favour a proposal by the United Nations that would use voter records from 2009, but only for a four year period till the Kirkuk issue can be further clarified.

"The subject could not be settled today and we in the Kurdish alliance, we support the UN suggestion," said Othman.

Iraqi politicians have continually delayed discussing how to resolve Kirkuk as the Arab-dominated central government and the Kurdish politicians of the northern autonomous region cannot agree on its future.

It has been during periods of political deadlock like these that Iraq becomes particularly vulnerable to renewed violence.

In 2006, months of political wrangling over the country's first permanent post-invasion government allowed al Qaeda linked insurgent groups to provoke Shiite militias into a near-civil war that tore the country apart.

The last few months have seen an upsurge in violence by al Qaeda in Iraq.

Sunday's car bombings, targeting the Justice Ministry and the Baghdad provincial government building, were the worst in more than two years and came a little more than two months after another series of bombs targeted government buildings in Baghdad and also killed more than 100 people.

Late Monday, the militant group known as the Islamic State of Iraq said in a statement posted on the Internet that claimed responsibility for this week's attacks. It said its "martyrs ... targeted the dens of infidelity."

The posting said the group's suicide bombers targeted the "pillars of the Safawi and rejectionist state in the land of caliphate," referring to the Shiite government in Baghdad and its close ally, Iran.

"One of these selected targets that were hit this time was the 'Ministry of Injustice and Oppression,' the so-called Ministry of Justice, along with the Baghdad Provincial Council," the statement said.

The authenticity of the statement, which appeared on a Web site commonly used by militants, could not be independently confirmed. The same group also claimed responsibility for the August.

Linked to the wider terror network, the Islamic State of Iraq is an umbrella group within the Arab country that comprises a militant coalition with al Qaeda as a leading member.

The attack Sunday raised more fears about the country's ability to protect itself as the U.S. military prepares to withdraw.

Among the dead were two dozen children, killed on a bus that was leaving a daycare centre inside the Justice Ministry, said a local police official and an official at the hospital where the bodies were brought. Both spoke on condition of anonymity because they were not authorized to talk to the media.

Some sort of agreement over the law that will allow elections to proceed could mollify public anger over the government's performance on security and other critical issues.

The other big sticking point over the electoral law is whether people would vote on individual candidates or simply by party names. The so-called "open list" is perceived by many voters as being more transparent, and has the support of Prime Minister Nouri al-Maliki who fared well under a similar system used during provincial elections earlier this year.

Kurdish parties prefer closed, party-list voting, which plays into their organizational strength across the autonomous region.