The statement apparently made by Omar Bin Laden has appeared on an online monitoring service.
Omar, who is Bin Laden's fourth eldest son, claimed he and the Al Qaeda chief's other children are reserving the right to take legal action in the U.S. and internationally to 'determine the true fate of our vanished father', the SITE Intelligence Group said.
He also branded his father's burial at sea as a 'humiliation' for his family.
There was no independent confirmation of the authenticity of the letter. It was published on the website of Islamist ideologue Abu Walid al-Masri.
Several specialists on militant propaganda said the text appeared genuine.
The news came as it emerged the CIA will allow a select few lawmakers to view the controversial pictures of Osama Bin Laden's corpse.
The CIA will allow the group to see the photos only if they travel to the agency's headquarters.
The move came as the White House faced renewed pressure to release the grisly images, following a series of requests filed under the Freedom of Information Act.
News organisations, public interest groups and even one politician have all lodged official demands with government agencies to see the photographs of Bin Laden's body after he was shot dead last week at the Abbottabad compound in Pakistan.
President Obama has so far strongly resisted calls to release the pictures as 'proof' of the terror chief's death at the hands of U.S. special forces.
He and his wife - formerly known as Jane Felix-Browne, but who now goes by the name Zaina Bin Laden - did not respond to emailed and telephoned requests for comment.
In April it was announced that a former British pole dancer has become pregnant with the couple's baby through IVF.
Louise Pollard, who is now a PA who lives in London, miscarried twins for the couple last year.
Omar and Zaina split up afterwards amid claims that he was suffering from a mental illness, but it now appears they are back together despite Omar telling the Daily Mail in September that there was 'no chance' of a reconciliation.
The letter purporting to be from Omar said, in part: 'We hold the American President (Barack) Obama legally responsible to clarify the fate of our father, Osama Bin Laden, for it is unacceptable, humanely and religiously, to dispose of a person with such importance and status among his people, by throwing his body into the sea in that way, which demeans and humiliates his family and his supporters and which challenges religious provisions and feelings of hundreds of millions of Muslims.'
The letter said the U.S. administration had offered no proof to back up its account of the mission.
It alleged the goal of raid had been to kill and not arrest, adding that afterwards the American commandos had 'rushed to dispose of the body'.
Some Muslims have misgivings about how U.S. forces killed Bin Laden in a raid in Pakistan on May 2 and disposed of his body in the ocean.
Questions have multiplied since the White House said the Al Qaeda leader was unarmed when U.S. helicopter-borne commandos raided the villa where he was hiding in the city of Abbottabad.
Bin Laden's swift burial at sea, in what many Muslims say was a violation of Islamic custom, has also stirred anger.
