They claim his body was taken by members of Skull and Bones, a secret student society, and are hidden at Yale University.
George W Bush’s grandfather and two other members of the group are said to have taken the remains of the Apache warrior Geronimo during the First World War.
However, the society’s repeated refusal to comment on the story, or on rumours that new members have to kiss the chief’s skull, have prompted the extraordinary lawsuit.
In a court action that names not only Yale and the society, but also Barack Obama and Robert Gates, his defence secretary, 20 descendants of the famous American Indian leader are seeking to recover his remains so his spirit can be laid to rest in his tribal homeland.
Their legal action, filed this week in a federal-district court in Washington DC on the 100th anniversary of his death, will seek to determine the truth of rumours that Geronimo’s burial at Fort Sill in Oklahoma was not his final resting place.
Three Bonesmen, including Prescott Bush, served at Fort Sill during the First World War.
The trio were rumoured to have dug up Geronimo’s remains in 1918 and took some of them back to Yale where they are supposedly still kept in the society’s hall – known as the “Tomb” – on the university campus.
The Skull and Bones, whose illustrious membership has numbered three US presidents including both Bushes, supposedly makes new members kiss the Chiricahua Apache’s skull.
The lawsuit – which also names Pete Geren, the Army Secretary, as a defendant – seeks to “to free Geronimo, his remains, funerary objects and spirit from 100 years of imprisonment at Fort Sill, Oklahoma, the Yale University campus at New Haven, Connecticut and wherever else they may be found”.
Mr Obama and his colleagues were included in the action because Geronimo was initially buried on US government land.
The remains would be returned to Geronimo’s birthplace in the Gila Mountains of New Mexico for a traditional Apache burial, said his great-grandson, Harlyn.
He stressed that such a burial was one of the most important sacred rites in his tribe’s culture.
“It’s been 100 years since the death of my great-grandfather in 1909. It’s been 100 years of imprisonment,” Mr Geronimo said outside court.
“The spirit is wandering until a proper burial has been performed. The only way to put this into closure is to release the remains, his spirit, so that he can be taken back to his homeland in the Gila Mountains, at the head of the Gila River.” The suit contends that Geronimo’s descendants are entitled to his remains and funerary possessions under the 1990 American Indian Graves Protection and Repatriation Act.
The Geronimo family are being represented by Ramsey Clark, who was attorney general under President Lyndon Johnson.
“In this lawsuit, we’re going to find out if the bones are there or not,” he said.
Mr Geronimo said he hoped the people named in the suit would take it seriously.
A spokesman for Yale said the university had “no relics or bones belonging to Geronimo” but stressed it could not answer for Skull and Bones because it was independent. The society has so far refused to comment.
Aged 79, Geronimo died of pneumonia in 1909 as a prisoner of war at Fort Sill after decades spent fighting against US and Mexican expansion into Apache lands.
Skull and Bones, about which George W Bush once wrote that it was “so secret, I can’t say anything more”, has never said whether any of Geronimo’s remains are in its possession.
However, in 2006, the Yale Alumni magazine published a letter written at the time of the alleged grave robbery in which a Skull and Bones member confirmed that Geronimo’s skull, femurs and some of his riding gear had been taken to the society’s hall.
The letter prompted Harlyn Geronimo to write to President Bush, but he said he never got a reply.