The claim by US war veteran Jim Brown was made during an interview included in a 30-minute current affairs report to be broadcast by Italian state news channel RaiNews24 on Thursday.
Brown told the Italian news channel that the bombing took place on the last day of the war in Iraq on 27 February 1991.
RaiNews24 claims to have conducted its own inquiry and found that a seismic event took place on that day equal to a five-kilotonne blast.
The network cited the online archives of the International Seismological Center, a non-profit UK-based organisation, as confirmation of its research.
The Italian journalist in charge of the inquiry Maurizio Torrealta told Adnkronos International (AKI) that there is no definitive proof of the nuclear blast and that it should not be taken as a fact.
Instead he asked the international community to further investigate the claims by Brown.
"We are asking journalists and the international community for help, in order to clarify this," said Torrealta.
However, in the documentary, which was shown to the media on Wednesday, Torrealta said that one of the possible reasons that the US may have dropped the bomb, was in retribution for the launch of Scud missiles on the US Dhahran military base in Saudi Arabia on 25 February.
Twenty-eight American soldiers died in the attack.
The US veteran, Jim Brown was not present during the alleged launch of the bomb and it is not clear how he obtained the information.
RaiNews24 said that 45-year-old Brown was originally a fourth-level engineer in the US Army and was demoted to third-level after health problems, following a vaccination against chemical weapons.
The injection deteriorated his health and he was eventually discharged from the army with honour.
He is now director of the GulfWatch I.N.S. organisation. Its website claims to have 350 supporters who are or were involved in coalition intelligence during the 1991 Gulf War.
"These people have agreed to work together to make sure that as much information about the war as possible is released about the activities prior to, during and after the war that have affected the health of potentially hundreds of thousands of soldiers, and their spouses and children," said a statement on the website.
The documentary included an interview with an Iraqi doctor, Jawad al-Ali, who told RaiNews24 that before the beginning of the first Gulf War in 1989 there were 32 cases of tumours, while in 2002 the number had risen to 600 in the Basra area.
Al-Ali also told RaiNews24 that tumours that used to affect older citizens had started to impact younger children. He then showed alleged photos of the tumours in the documentary.
During the RaiNews24 report , Torrealta said that the US State Department had rejected Brown's claims and said only 'conventional' weapons had been used during the first Gulf War.