Interim Iraqi prime minister Iyad Allawi hailed the election as "the start of a new era" as he cast his vote yesterday.

But with insurgents threatening a long term war, the United States and Allawi's government have refused to set a timetable to withdraw the invasion force which deposed Saddam Hussein two years ago.

Shia and Sunni Muslim political parties -- who have largely boycotted the election -- face much wrangling with Kurdish and secular rivals over the makeup of the new government and the writing of a constitution.

US President George W. Bush hailed the courage of Iraqis, saying "the advent of democracy in Iraq will serve as a powerful example to reformers throughout the entire Middle East."

The US-led coalition hopes the building up of a strong Iraqi force will blunt the threat of Abu Musab al-Zarqawi and other extremists. But many US military leaders are cautious.

"We should not delude ourselves here," said Brigadier General Doug Lute, director of operations for US Central Command which runs the US military operation in Iraq and Afghanistan.

"When we wake up on January 31, Iraq is still going to be a violent place, and it's still going to have an emerging government, and it's still going to have relatively immature security forces.

"The elections themselves are not going to prove to be a panacea."

The new leaders that come out of the election will have to fear for their lives and they also face tight political deadlines.

The 275-member national assembly has to elect a president and two deputies by a two-thirds majority.

The three-man presidency council will then have two weeks to choose a prime minister and cabinet, which must get a national assembly vote of confidence.

The assembly has until August 15 to write a draft constitution that will have to be put to a referendum by October 15.

If the referendum succeeds with a two thirds majority then an election for a permanent government will be held in December. If it fails, the whole process starts again.

If opinion polls are right, the United Iraqi Alliance, which has the blessing of the leader of the majority Shia community, Grand Ayatollah Ali al-Sistani, should emerge as the biggest single force in the assembly.

But it is not certain to get a majority if the Kurdish, Sunni and other secular parties do well. There is also doubt that the alliances on Sistani's list will hold once the vote is over.

Coalition officials admit that leaves open the possibility of weeks of tense talks over the makeup of the government.

"There is a lot of horse-trading to come," one senior US official said.

The United States has sought to persuade Shia leaders to find a way to bring Sunni officials who have boycotted the election into the constitutional process.