In Baghdad, they believe that the dictator is alive and probably not too far away

The men who stood peering deep into the bomb crater all agreed on one thing: the man the bomb had been sent to kill was still alive and probably living not too far away.

"I think he is still in Baghdad. No one can tell what happened. There are no facts," said Zuhair al-Hadithi, a shop owner. "Many people here have been saying he is alive."

He, of course, is Saddam Hussein, and in the aftermath of the surrender of Iraq's former deputy prime minister Tariq Aziz, the hunt for the former president is more pressing than ever. There have been no authenticated sightings of him for weeks and, although many Iraqis appear to believe he is alive and planning some sort of counter-attack, the truth may be that the dictator is already dead – killed or fatally wounded in the first strikes of the war.

In that first volley, the United States used Stealth bombers and at least 30 cruise missiles against a compound in Baghdad where Saddam, his sons and members of his senior leadership were thought to be meeting. The strike was a dramatic switch in American battle plans but the US President, George Bush, believed there was a chance to kill the Iraqi leader at the start of the war.

In his television interview, Mr Bush said Saddam was possibly killed in that first volley. "The people will wonder if Saddam is dead or not. There's some evidence that ... suggests he might be. We would never make that declaration until we were more certain, but the person who helped direct the attacks believes Saddam at a very minimum was severely wounded."

The agent working for America on the ground in Baghdad was convinced Saddam and his two sons, Uday and Qusay, would be there. He also told the Pentagon that the strike had been successful and that Saddam had at the very least been wounded.

"We had some evidence ... that strikes from the first day may have gotten him. I say 'may' because we don't have the DNA in hand to prove [it]," Mr Bush said.

The complex attacked in the first strike of the war is not the only location struck by US warplanes where American forces have been searching for DNA samples that may prove to them that Saddam was hit. At the rear of al-Sa'ah (the clock) restaurant in the Mansur district of Baghdad lies a crater caused by a US "bunker-buster" bomb that was dropped in the early days of the war.

The locals gathering round it yesterday said there were rumours that the nearby restaurant had been owned by Uday, though staff denied it. They agreed, however, that the upstairs part of the restaurant was used by senior Iraqi officials from the secret police and the Baath party. "Maybe they thought there was a meeting here," said Hamid, a waiter. "Many of the senior people came here for food." The bomb was certainly deadly. Locals say it killed 18 people – the body of the most recently discovered victim, a child, was only recovered earlier this week – though none believes that the dictator was among them.

"If he had been killed we would know about it by now," said Rahab Mohammed. "We hope he is alive and we hope he returns. We will love Saddam Hussein until the last drop of blood we have."

The Iraqi National Congress (INC), one of many political groups made up of formerly exiled Iraqis now vying for power, said it has been receiving regular reports of sightings of Saddam and that intelligence operations were actively pursuing him in a broad swath of the country towards the border with Iran.

A man said to be the deposed dictator was also reportedly caught on video footage, speaking to people at a mosque in the Azamiyah district of the city, the day after US forces rolled into the centre of Baghdad.

Mr Bush said his analysts told him they did not believe the reports to be true.