Three former members of the Exclusive Brethren have asked a judge to order the arrest of the sect's leader Bruce Hales for genocide and people smuggling.
The former sect members told the Federal Court they have evidence that members of the secretive Christian fellowship have committed crimes against humanity, people smuggling and international organised crime.
Indian sisters Lydia and Rebecca Desai and Priscilla D'Souza say they also fear for their safety.
They have asked Federal Court judge, Justice Tony North, to order Australian Federal Police to arrest Mr Hales, the group's world leader, and two other senior sect members.
In documents filed with the court, the women also call for the extradition from New Zealand of their father Romulus Desai, who is still a member of the Brethren, and three other sect members.
The documents also ask the judge to order Prime Minister Kevin Rudd to petition the United Nations to bring international awareness about the genocide.
Lydia Desai told the court, sitting in Melbourne, the sect had committed genocide by targeting the beliefs of a minority group which they are associated with - Boss Kingdom schools in India.
They do not claim the genocide is in the form of mass deaths, but in the form of the destruction of their religious group.
The women also accuse the group of debt bondage, slavery and disrupting the integrity and security of the international community and foreign governments.
The Exclusive Brethren Church rejected the claims, saying the allegations are bizare and baseless.
"The applicants' attempt to file a similar application in the High Court of Australia failed earlier this year and did not even make it to a hearing," the church said in a statement.
The sisters, who have New Zealand residency, have taken action in an Australian court because Mr Hales is an Australian citizen.
Justice North said he did not have the power to order the arrest, but said he would examine the law to see whether the Federal Court had power to order the police to investigate the matter.
Jeff Cranston, representing the police, said they needed more time to investigate the court's powers.