The 42,000-year-old remains, which had been stored in the Mungo National Park in western NSW, were buried on May 24 despite a pending legal challenge.
A group of traditional owners, made up of Mutthi Mutthi, Barkandji and Ngiyampaa elders, lodged an emergency application with then environment minister Sussan Ley on May 20 to prevent the burial under Indigenous heritage protection laws.
The federal government said NSW, which manages the World Heritage listed park, had assured them the burial would not go ahead while the application was under review.
But Mungo Man and Mungo Lady were buried days later.
Mutthi Mutthi man Jason Kelly, representing the elders, said there is great distress about the burials.
"We want to know where Mungo Man and Mungo Lady are and if they're safe," he told AAP.
In April, Ms Ley approved a plan from NSW Heritage and Indigenous organisation the Willandra Lakes Region Aboriginal Advisory Group to bury 108 ancestral remains in 26 unmarked graves.
Mr Kelly said the group of elders instead wanted the remains buried in a way to ensure preservation, with simple monuments, and the construction of a cultural centre.
That proposal was the result of decades of negotiation between elders and archaeologists, he said.
"After 20 to 30 years of deep conversations and fighting and sickness, we're able to reconcile and come up with this," he said.
"This was what we've all been fighting for."
The advisory group has been contacted for comment.
A representative of NSW Heritage said an external investigation is underway into the removal of the remains from storage and their burial.
The state government did not approve or conduct the burials and another 106 ancestral remains are being held under a new security arrangement, the official said.
"This is a sensitive matter which appears to involve a dispute within Aboriginal communities, and the NSW government is seeking to address the issues in a manner that recognises and respects the different views," they said.
Incoming Indigenous Australians Minister Linda Burney has been briefed.
Mr Kelly is hopeful the new Labor government will better engage with traditional owners.
"I would love to see the prime minister do with us at Mungo what Gough Whitlam did with the Aboriginal Tent Embassy.
"To go out and sit down with them directly himself."
Between the late 1960s and the 1980s, 108 remains were removed from the Willandra Lakes and Lake Mungo and taken to the Australian National University for study.
Mungo Lady was returned to the Mungo National Park for safekeeping in 1992, while Mungo Man was returned in 2017 with formal letters of apology to the traditional owners.
