The plaintiffs originate from Kineusu, a historic Ainu village on the southeastern coast of Hokkaido, and are demanding the return of remains taken from their kotan on the basis of tribal affiliation.
According to lawyer Morihiro Ichikawa, who is representing the group, this is a landmark case in Japan in terms of indigenous rights.
"This is the first case where the Ainu people have argued for their aboriginal title to be recognised in a Japanese court, and also the first time they have demanded the return of their ancestors' skulls and bones.
"So far, the Japanese courts have never handled Ainu rights cases," he says.
Under Japan's Civil Code, human remains can only be transferred to an individual who is a direct descendant or proven blood relative of the deceased, Morihiro explains.
"We are arguing that the bones of the kotan's members belong to the whole kotan as a tribe, not to an individual.
"Indeed, the Ainu didn't individually manage the bones after burials."
As Hokkaido University is a national university it stands on the same side as the Japanese Government and so far has refused to recognise aboriginal title, Morihiro says.
The circumstances by which the universities came into possession of the Ainu remains are somewhat murky, in part due to the large period of time which has elapsed since most of the exhumations occurred - 140 years in some cases.
Few reliable records remain which show the circumstances surrounding the taking of the remains, although some Ainu argue there is evidence that at least some of the bones were "stolen".
Hokkaido University vice-president Takashi Mikami rejects this claim and says they have found "no documents that suggest grave theft".
He does acknowledge the university could have done a better job of looking after the bones.
"There were problems in the way we managed the remains," he says.
The careless management of the Ainu remains, not just by Hokkaido University, but by most of the Japanese universities involved, is a key issue which is making the return of bones problematic and, according to the president of the Hokkaido Ainu Association Katou Tadashi, is causing the Ainu considerable distress.
"During the collection of these remains for research, many of the bones from different people were mixed together.
"Skulls were separated from bodies and also burial items were separated from the remains, making it impossible to know whom the bones belong to. This is very upsetting for us," he says.
Tadashi believes that the taking of the Ainu remains is a "serious human rights issue" and he wants to see all the bones returned as soon as possible.
Unlike in contemporary Japanese Buddhist ceremonies where cremation is the norm, traditionally Ainu have always buried the dead and, according to Tadashi, this is a way to ensure their "spirit remains connected to the family".
They also have a long-established tradition of practising ritual memorial ceremonies for their deceased ancestors at various times throughout the year.
These outdoor ceremonies, called icharupa, are performed to console the spirits of the ancestors and tonoto, or sacred sake, is sprinkled over the natural world using inau, or traditional offering sticks, and offerings of food, such as rice or sweets, are also made.
"As soon as possible, we want the remains of our ancestors returned so we can perform icharupa, says Tadashi. "I believe the most important thing is to comfort the souls of our ancestors."
A culture's decline
The Ainu are the indigenous people of Japan's northern island of Hokkaido and also the Kurile and Sakhalin Islands of Russia's far east.
They are a distinct ethnic group to the Yamato Japanese and have lighter skin, more body hair and rounder eyes, giving them a more European appearance, although recent DNA research suggests they are not actually Caucasian, but of "proto-mongoloid" genetic stock.
The Ainu were an ancient hunter/gatherer society with their own language, culture and a religion based on natural phenomenon - although it is believed there are now almost no native Ainu speakers left alive.
Until the 18th century, the Ainu lived in relative isolation on Hokkaido and maintained a society independent of the Japanese, although extensive interactions through trade, and some conflict, did occur.
Then after the Meiji Restoration in 1868, Hokkaido was formally annexed by the Japanese and in 1899 the Hokkaido Former Aborigines Protection Act was passed.
This law marked the beginning of the end of traditional Ainu culture and society, and led to forced assimilation of the Ainu into mainstream Japanese life and the loss of customary hunting and fishing rights.
It wasn't until 2008 that the Japanese diet finally passed a resolution formally recognising the Ainu as the indigenous people of Japan.
The current Ainu population of Japan is estimated to be somewhere between 25,000 and 200,000.