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"Several people were wounded, including members of parliament and some employees."
Later, security officials at parliament told AP that they believed the suicide bomber was a bodyguard of a Sunni MP who was not among the dead, although they would not name the parliamentarian concerned.
The officials also told the agency that two satchel bombs were found inside the building near the dining hall. An American military bomb squad was called and took the explosives away, detonating them without incident.
Ali al-Dabbagh, a government spokesman, suggested that those behind the attack might work in the building.
"There are some groups that work in politics during the day and do things other than politics at night," AP quoted him as telling the Iraqi Alhurra television station.
On a day of violence in the capital, in which one of Baghdad's major bridges was also destroyed, MPs described their shock at the extraordinary breach in security.
Mohammed al-Dayni, another member of the National Dialogue Front, told Iraqi television: "I am standing now at the site of the explosion and looking at the severed legs of the person who carried out the operation. If this tells us anything, it tells us that security is lax."
The attacker would have had to bypass several checkpoints and metal detectors, both at the entrance to the Green Zone and then at the parliament building, to bring an explosive device into the convention centre. Inspections are usually so rigorous that visitors to the building have to take the battery out of their mobile phone to show that it is not booby-trapped.
Witnesses said that sniffer dogs had been added to the security measures this morning, a rare precaution that suggested there were fears of a terrorist attack. On April 1, US troops discovered two suicide vests inside the Green Zone.
The enormous compound, which houses most of the international interests in Baghdad, as well as the key institutions of the Iraqi Government, has suffered periodic breaches of security since the US-led invasion of Iraq in 2003. But they have mostly been limited to explosions at the entrances and occasional rocket attacks.
Rockets killed two Americans, a soldier and a contractor, last month, a few days after another missile landed within 100 yards of where the UN Secretary-General Ban Ki-moon was holding a press conference. No one was wounded in that attack.
The White House condemned today's explosion and Condoleezza Rice, the US Secretary of State, said it would not deter American and Iraqi commanders from their joint effort to regain control of the streets of the Iraqi capital.
Operation Law and Order, reinforced by thousands of extra American soldiers and considered by many to be the last-ditch attempt to halt the endemic sectarian violence in Baghdad, has been shaken in the last 48 hours by gun battles and the destruction this morning of the al-Sarafiya bridge, one of the key crossing points over the Tigris river.
"We said there were going to be good days and bad days concerning the security plan," said Ms Rice. "But the commanders are carrying out their responsibilities and working to try to make the population more secure. We're really at the beginning of this and not the end of this."
The British Foreign Secretary, Margaret Beckett, said that she was "deeply shocked and saddened to hear of this appalling attack".
"Nothing could highlight more the twisted minds of those who are seeking to disrupt the democratic process in Iraq. Those who carry out these outrageous attacks offer nothing to the Iraqi people except more murder and destruction," she said in a statement.
"The Iraqi people have shown great fortitude and courage. They deserve our full and continued support."
President Bush later told reporters: “I strongly condemn the action. It reminds us, though, that there is an enemy willing to bomb innocent people and a symbol of democracy."
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