US officials admitted last night that the bombing of the Iraqi parliament shows that not even the heavily fortified Green Zone is safe any more, despite the security crackdown launched earlier this year in the Iraqi capital.

American and Iraqi security officials were last night investigating how a suicide bomber evaded a ring of security checks and blew himself up in the assembly's cafe, killing three MPs and five other people and wounding more than 20.

About 100,000 US and Iraqi soldiers are on the streets of the capital as part of the troop "surge" begun two months ago; while security inside the Green Zone has been tightened following the recent discovery there of two suicide bomb belts.

But after the deadliest attack ever in the Green Zone, US officials warned that nowhere is safe in Baghdad. "The international zone is not safe, it is just safer than the rest of the city," said Lieutenant Colonel Christopher Garver. "Enemies of the country are trying to drive a wedge between the people and the government." In Washington the secretary of state, Condoleezza Rice, said: "We know that there is a security problem in Baghdad. This [crackdown] is still early in the process and I don't think anyone expected that there wouldn't be counter-efforts by terrorists to undermine the security presence."

The blast came hours after a suicide truck bomb exploded on a major bridge in northern Baghdad that links the east and west of the city. The steel structure collapsed and sent cars tumbling into the Tigris river, killing at least 10 people.

The parliament bomber struck at around 2.30pm as lawmakers and government officials gathered for lunch on the first floor. The Saddam-era building also houses Iraqi government offices and has withstood repeated mortar attacks since March 2003. Barzan Mohammed, an assistant to the deputy speaker of parliament, Arif Tayfour, said: "I was just leaving my office for lunch and there was this very big bang. I ran along the corridor to the restaurant but all I could see were huge clouds of dust. It was choking and there was the smell of burning meat.

"The windows were blown out, there were tables and chairs everywhere and the sound of groaning. Then I saw that many people had been hit, and that blood was everywhere."

Major General William Caldwell, the chief US military spokesman, said witness accounts pointed to a suicide attack but "we don't know at this point who it was. We do know in the past that suicide vests have been used predominantly by al-Qaida." Initial reports said the explosion was near the cash register and there was speculation a cafe worker had smuggled in a bomb in food boxes. But Mohammed Abu Bakr, who runs the parliamentary media unit, and other witnesses said they saw two legs on the floor. "None of those killed or wounded lost their legs," he said.

A police source said they had found the remains of what appeared to be a suicide belt, and the bomber was believed to have been a man. The building was sealed after the blast and MPs were told to stay where they were for fear of a second blast.

Among the dead MPs was Mohammed Awad, a member of the hardline Sunni National Dialogue Front, which holds 11 seats in the legislature and is harshly critical of the Shia-led government of the prime minister, Nuri al Maliki. Another was Taha al-Liheibi, of the Sunni Accordance Front, which holds 44 seats and is part of the National Unity government. The third was Omar Ali al-Hussein, a member of the Kurdistan Islamic Union.

Iraq's parliament is surrounded by concentric rings of checkpoints that start from the outer borders of the Green Zone. Police were looking into reports that a security scanner checking pedestrians at the entrance near the parliament building was not working yesterday morning, and that people were searched by hand and metal detectors instead.

Once past these outer hurdles there is a further check at the door of the building itself. Dogs sniff for explosives, handbags and briefcases are checked and put through a scanner, and individuals are patted down by guards to check for weapons. Everyone who enters, including MPs, must have a pass or be escorted by someone with valid credentials.