General David Petraeus told the BBC he was "absolutely certain" Mr Moore and the other hostages were held in Iran for part of their period in captivity and the Guardian quoted a former member of Iran's Revolutionary Guard as saying the kidnapping was masterminded by the organisation.
But the Foreign Office played down the reports today and said there was no evidence the British hostages were held in Iran following their abduction.
BBC security correspondent Frank Gardner put the question directly to Gen Petraeus, who was commander of multi-national forces in Iraq at the time of the kidnap and now heads US Central Command, at a conference in Bahrain on December 13.
Mr Gardner told Radio 4's Today programme: "He didn't hesitate. He said 'I'm absolutely certain. I'm 90% certain'.
"I said is this a personal view or have you seen hard intelligence, and he thought for a minute and he said 'I am pretty sure I've seen hard intelligence on it' ... that they were held in Iran for some of the period of their captivity."
There were also reports today that Mr Moore was targeted for abduction because he was in Iraq to install computer systems to track the movements of money within the post-war administration which might have shown how funds supplied by the US and its allies were being diverted to Iranian-backed insurgent groups.
The Guardian claimed the men were moved to Iran within days of their kidnapping and held by the Guard's al-Quds brigade at the Qasser Shiereen military camp near the Iraqi border and then at a camp called Tehran Pars near the city of Qom.
"It was an Iranian kidnap, led by the Revolutionary Guard, carried out by the al-Quds brigade," said the unnamed former Guard member.
"My contact works for al-Quds. He took part in the planning of the kidnap and he watched the kidnapping as it was taking place. He told me that they spent two days at the Qasser Shiereen camp. They then took them deep inside Iran."
But the Foreign Office said: "We have no evidence that the British hostages, including Peter Moore, were held in Iran. We are not in a position to say with any certainty where they were held during each and every single day of their two-and-a-half years in captivity."
The reports will further heighten tension between the UK and Iran after Britain renewed its calls for human rights to be respected over the clampdown on protesters in Tehran and other cities.
The UK's ambassador in the country, Simon Gass, responded "robustly" after being summoned by the Tehran regime over Foreign Secretary David Miliband's praise for the "courage" of demonstrators.
As diplomatic tensions rose, Iran's foreign minister Manouchehr Mottaki said Britain would "receive a punch on the mouth" if it does not "stop its nonsense".
The regime has consistently blamed other countries, including Britain, for fomenting the violent opposition protests which have been taking place since the disputed presidential election.
Following his surprise release yesterday morning, Mr Moore spent the night at the British Embassy in Baghdad, where he is receiving medical attention and support ahead of his return home. The Foreign Office was unable to say whether he would fly back to Britain today.
The 36-year-old computer expert from Lincoln is believed to have been in solitary confinement for most of the last 31 months, since being kidnapped along with his four British bodyguards by militants posing as police at the finance ministry in Baghdad on May 29 2007.
Family members indicated yesterday that he did not know the fate of his four fellow captives.
The bodies of Alec MacLachlan, Jason Swindlehurst and Jason Creswell were passed to British authorities earlier this year and the Foreign Office believes the fourth - Alan McMenemy - is also dead.
Speculation was mounting that Mr Moore was freed in return for the release from US custody of a leading Shi'ite insurgent.
Qais al-Khazali is a leader of the Asaib al-Haq group, which is believed to be behind the abduction of the five Britons, and it is thought that his release was one of the kidnappers' key demands.
He was handed over to Iraqi authorities along with a number of other detainees, and officials said he would be set free unless evidence is found to support a prosecution in the domestic legal system.
Mr Miliband insists that no "substantive concessions" were made to the hostage-takers by the UK, and the Foreign Office said last night that Mr Moore's release was "completely separate" from the handover of Khazali which took place under the terms of an agreement between the US and Iraqi governments.
Khazali and his brother Laith have been linked to the killing of five US soldiers in Karbala in 2007 and Asaib al-Haq - or League of Righteousness - has since been blamed for a number of attacks.
Shortly after Laith's release in June, the remains of Mr Creswell and Mr Swindlehurst were passed to UK officials by the Iraqi authorities.
Mr Moore's mother Avril Sweeney said last night his release had lifted "a big black cloud" hanging over his family.
Speaking from her home in Thornton Cleveleys, Lancashire, 54-year-old Mrs Sweeney said the years of his imprisonment had been "horrendous", adding: "All I want to do now is to see him back."
Mr Moore's father Graeme, 60, from Wigston, Leicestershire, said he was "over the moon" at the news.
He said: "We are so relieved and we just want to get him home, back now to his family and friends."
Mr Moore's first request after arriving at the UK Embassy yesterday was for some British food before calling his family, the Independent reported.
"Thank God, you are the first British faces I have seen for years. I just want to cry," he is reported to have said.
Both Mr Miliband and Prime Minister Gordon Brown issued demands for the kidnappers to return Mr McMenemy's body.
The Prime Minister's human rights envoy to Iraq, Labour MP Ann Clwyd, said reports of direct Iranian involvement in the kidnapping were "very worrying".
But she said she had heard no evidence to support it during a recent visit to Baghdad to discuss the hostage issue with President Jalal Talabani and deputy prime minister Rafi al-Issawi.
Ms Clwyd told BBC Radio 4's Today programme: "I heard the rumours, and there are lots of rumours, of course, in Iraq on all sorts of issues, but I personally didn't talk about Iran."
Talks in the summer between Iraqi prime minister Nouri al-Maliki and the Asaib al-Haq group collapsed because of the refusal to release Khazali, said Ms Clwyd, though she could not confirm that Mr Moore's release was directly linked to the militant's removal from US custody.
She said she understood that Asaib al-Haq had given up its campaign of violence and was hoping to put up candidates in elections in March.
"The Government of Iraq is carrying out a process of reconciliation with groups willing to renounce violence who want to enter the political mainstream," said Ms Clwyd.
"Obviously, hostage-taking is not compatible with political reconciliation."
