The prince's communications secretary said Harry has not expressed any views about the Iraq Historic Allegations Team's (IHAT) work.
A senior source was quoted in the Sun's report on 17 October, saying Harry was "furious" with the investigation.
The Sun would not comment on Harry's denial but stands by the story.
Speaking to the newspaper, the source said Prince Harry was "furious at the treatment of some British troops" and "frustrated" he could not intervene.
They added: "He thinks the whole thing is a joke and is very concerned about the support these men and women are getting."
But Prince Harry's communications secretary Jason Knauf said the prince was passionate about his work in supporting veterans and that it will be "a cause he champions for the rest of his life".
But Prince Harry, who served as an Army officer for 10 years and was deployed twice to Afghanistan, wanted to respond to the claims because it was "only fair that people know the facts".
Mr Knauf denied that Harry had spoken about his views on the topic to anyone as he didn't think it was appropriate.
He said: "Prince Harry does not comment on issues like this because to do so would actually undermine his ability to support veterans both in the UK and overseas."
Established in November 2010, IHAT was set up to investigate allegations of murder, abuse and torture of Iraqi civilians by UK military personnel between 2003 and 2009.
The claims have ranged from ill-treatment during detention to assault and death by shooting with some wrongdoing being exposed.
However in September, Prime Minister Theresa May said every effort must be made to stop the legal system being abused over allegations of serious misconduct by UK troops.
The prime minister told defence chiefs she was determined to stop "vexatious" claims being brought against the armed forces.
Last month she raised concerns over the "industrial scale" of claims lodged with IHAT.
More than 1,500 individuals have put in a claim to the body, with 326 cases being settled, and around Â£20 million being paid in compensation.
Prince Harry has denied that he told friends an investigation into allegations UK troops abused Iraqi civilians is "a joke".