Suicide bombings at polling stations and rocket attacks have failed to prevent Iraqis turning out in larger than expected numbers to vote in national elections.

Despite 33 deaths in at least nine suicide attacks, national voter turnout was at one point thought to be as high as 72 per cent, although later in the day Iraq’s Electoral Commission issued a revised estimate of about 60 per cent - still higher than most had predicted.

The voter figures were most impressive in in Shia and Kurdish areas, the communities oppressed under Saddam Hussein's Sunni regime, but UN election observers also reported queues outside polling stations in the northern city of Mosul, which has been torn by violence since the summer.

A handful of voters turned out even in the former rebel strongholds of Fallujah and Ramadi.

Many of the voters were women, some shrouded in black robes while others appeared to have dressed up in their finest clothes and brought their families with them to celebrate the country's first free, multi-party elections in half a century.

They queued patiently, under the gaze of heavily armed soldiers and police guarding the polling stations, to fill in their ballot paper and to have their forefinger marked with indelible blue ink to show that they had cast their vote.

"According to first reports we're getting, participation seems to be exceeding expectations in some parts of the country, " said Carlos Valenzuela, a UN election adviser who has spent the last 13 years organising polls in trouble spots around the world.

"There have been a number of attacks of course, as expected. These attacks have not stopped operations."

Mr Valenzuela added that although some polling stations initially failed to open in western Baghdad, and in the stretch of Sunni towns south of the capital known as the Triangle of Death, this problem was later "solved".

Some 14.2 million Iraqis were registered to voted, at more than 5,000 polling stations, to choose a 275-strong National Assembly and governing councils in 18 provinces. Voters in the Kurdish areas are also electing a regional parliament.

Militant groups tried unsuccessfully to sabotage the election, mounting at least nine suicide attacks and in some towns attacking polling stations with mortar fire.

In all but one case, militants were forced to use "human bombs" - men rigged with explosives - rather than cars, because of a nationwide driving ban imposed as an election security measure.

The deadliest attack occurred when a bomber with explosives strapped to his body blew himself in a queue at a polling station in the neighbourhood of Zayiuna in eastern Baghdad, killing nine people – seven civilians and two policemen - and himself. Twelve others were wounded.

A group led by Abu Musab al-Zarqawi, the Jordanian militant linked to al-Qaeda, claimed responsibility for attacks in Baghdad, Mosul, Samarra and Baqouba, in an internet statement whose genuineness could not be verified. The statement continued that the rebels had successfully "spoilt the election wedding".

Amid tight security, the streets of the capital resembled a war zone. Thousands of Iraqi forces, checkpoints and nearly 15,000 US troops patrolled as American attack helicopters circled overhead, and the roar of fighter jets from high above mingled with the thuds of explosions.

Turnout was low at first, as many Iraqis waited to see whether rebels carried through with their threats of violence. Most streets in Baghdad were deserted and shops closed. Concrete blast barriers blocked major roads.

But as the day wore on, voters gathered in greater numbers, and in many places were still queueing when polls closed at 5pm (2pm GMT).

There were even signs of enthusiasm. At one polling place in Baghdad, Iraqi soldiers and voters joined hands in a dance, while another polling station in the capital ran out of ballot papers and had to try urgently to get more.

Ayad Allawi, the interim Prime Minister, said: "This is a historic moment for Iraq, a day when Iraqis can hold their heads high because they are challenging the terrorists and starting to write their future with theire own hands."

Condoleezza Rice said later that President Bush was "incredibly encouraged" by the way that polling had gone. Washington was watching the election closely, hoping to hasten the day when the United States brings home its 150,000 soldiers.

Turnout was good even in areas where Sunni Muslims live alongside Shias, despite calls from several Sunni parties for boycotts of the polls. A spokesman for one Sunni group was subdued about the apparent failure of the boycott.

"The association's call for a boycott of the election was not a fatwa (religious edict), but only a statement," said Association of Muslim Scholars spokesman Omar Ragheb. "It was never a question of something religiously prohibited or permitted. We never sought to force anyone to boycott."

A Shia alliance formed under the guidance of the top Shi'ite cleric, Ayatollah Ali al-Sistani, is almost certain to win the most votes.

After the votes are counted a 275-member National Assembly will be formed, its seats allocated by proportional representation. Election organisers say it might be 10 days or more before they can announce final results.

The assembly will elect a president and two deputy presidents, who must have the backing of two-thirds of the assembly. The three-person council must then unanimously select a prime minister within two weeks, and appoint a cabinet.

The prime minister and cabinet will seek a vote of confidence from the National Assembly, to permit it to start start work.

The National Assembly will draw up a draft constitution for Iraq by August 15, which must be put to the Iraqi people for approval in a referendum to be held no later than October 15. If the constitution is approved, a general election will be held by December 15, and a new government installed by the end of the year.

If the constitution is rejected, the National Assembly will be dissolved and an election for a new one will take place by December 15.

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