They said that as many as five of the dead prisoners were Iraqis, two of whom came from Samarra, a volatile town to the north of the capital, where an attack by insurgents on the home of Mr Al-Naqib killed four of the Interior Minister's bodyguards on June 19.
The Herald has established the names of three of the prisoners alleged to have been killed. Two names connote ties to Syrian-based Arab tribes, suggesting they were foreign fighters: Ahmed Abdulah Ahsamey and Amer Lutfi Mohammed Ahmed al-Kutsia.
The third was Walid Mehdi Ahmed al-Samarrai. The last word of his name indicates that he was one of the two said to come from Samarra, which is in the Sunni Triangle.
The three names were provided to the Interior Ministry, where senior adviser Sabah Khadum undertook to provide a status report on each. He was asked if they were prisoners, were they alive or had they died in custody.
But the next day he cut short an interview by hanging up the phone, saying only: "I have no information - I don't want to comment on that specific matter."
All seven were described as young men. One of the witnesses spoke of the distinctive appearance of four as "Wahabbi", the colloquial Iraqi term for the foreign fundamentalist insurgency fighters and their Iraqi followers.
He said: "The Wahabbis had long beards, very short hair and they were wearing dishdashas [the caftan-like garment worn by Iraqi men]."
Raising the hem of his own dishdasha to reveal the cotton pantaloons usually worn beneath, he said: "The other three were just wearing these - they looked normal."
One witness justified the shootings as an unintended act of mercy: "They were happy to die because they had already been beaten by the police for two to eight hours a day to make them talk."
After the removal of the bodies, the officer in charge of the complex, General Raad Abdullah, is said to have called a meeting of the policemen and told them not to talk outside the station about what had happened. "He said it was a security issue," a witness said.
One of the Al-Amariyah witnesses said he watched as Iraqis among the Prime Minister's bodyguards piled the prisoners' bodies into the back of a Nissan utility and drove off. He did not know what became of them. But the other witness said the bodies were buried west of Baghdad, in open desert country near Abu Ghraib.
That would place their burial near the notorious prison, which was used by Saddam Hussein's security forces to torture and kill thousands of Iraqis. Subsequently it was revealed as the setting for the still-unfolding prisoner abuse scandal involving US troops in the aftermath of the fall of Baghdad.
The Herald has established that as many as 30 people, including the victims, may have been in the courtyard. One of the witnesses said there were five or six civilian-clad American security men in a convoy of five or six late model four-wheel-drive vehicles that was shepherding Dr Allawi's entourage on the day. The US military and Dr Allawi's office refused to respond to questions about the composition of his security team. It is understood that the core of his protection unit is drawn from the US Special Forces units.
The security establishment where the killings are said to have happened is on open ground on the border of the Al-Amariyah and Al-Kudra neighbourhoods in Baghdad.
About 90 policemen are stationed at the complex, which processes insurgents and more hardened offenders among those captured in the struggle against a wave of murder, robbery and kidnapping in post-invasion Iraq.
The Interior Ministry denied permission for the Herald to enter the heavily fortified police complex.
The two witnesses were independently and separately found by the Herald. Neither approached the newspaper. They were interviewed on different days in a private home in Baghdad, without being told the other had spoken. A condition of the co-operation of each man was that no personal information would be published.
Both interviews lasted more than 90 minutes and were conducted through an interpreter, with another journalist present for one of the meetings. The witnesses were not paid for the interviews.
Dr Allawi's office has dismissed the allegations as rumours instigated by enemies of his interim government.
A statement in the name of spokesman Taha Hussein read: "We face these sorts of allegations on a regular basis. Numerous groups are attempting to hinder what the interim Iraqi government is on the verge of achieving, and occasionally they spread outrageous accusations hoping they will be believed and thus harm the honourable reputation of those who sacrifice so much to protect this glorious country and its now free and respectable people.
"Dr Allawi is turning this country into a free and democratic nation run by the rule of law; so if your sources are as credible as they say they are, then they are more than welcome to file a complaint in a court of law against the Prime Minister."
In response to a question asking if Dr Allawi carried a gun, the statement said: "[He] does not carry a pistol. He is the Prime Minister of Iraq, not a combatant in need of any weaponry."
Sabah Khadum, a senior adviser to Interior Minister Mr Naqib, whose portfolio covers police matters, also dismissed the accounts. Rejecting them as "ludicrous", Mr Khadum said of Dr Allawi: "He is a doctor and I know him. He was my neighbour in London. He just doesn't have it in him. Baghdad is a city of rumours. This is not worth discussing."
Mr Khadum added: "Do you think a man who is Prime Minister is going to disqualify himself for life like this? This is not a government of gangsters."
Asked if Dr Allawi had visited the Al-Amariyah complex - one of the most important counter-insurgency centres in Baghdad - Mr Khadum said he could not reveal the Prime Minister's movements. But he added: "Dr Allawi has made many visits to police stations ... he is heading the offensive."
US officials in Iraq have not made an outright denial of the allegations. An emailed response to questions from the Herald to the US ambassador, John Negroponte, said: "If we attempted to refute each [rumour], we would have no time for other business. As far as this embassy's press office is concerned, this case is closed."