"We have offered a deal to Suharto's family ... that the civil case related to the Supersemar foundation will be settled out of the court," Hendarman Supanji told reporters.
But OC Kalgis, Suharto's lawyer, told Al Jazeera that the former president's family had rejected the government's offer.
"We have rejected [it] becuase the state has not managed to give any evidences about its claims in the civil court ... we reject absolutely an out of court settlement," he said.
A criminal case against Suharto was abandoned in 2006 due to his persistent poor health but the civil suit, launched last year, was seeking $1.4 billion in damages and returned stolen assets skimmed off the foundation.
Supanji said he had met with the family of Suharto under the orders of President Susilo Bambang Yudhoyono. Under Indonesian law, if a defendant dies during such a civil suit, his or her family must instead defend the case.
"If we settle the case in court, it means that there's one loser and the other wins and the process will be quite long. But if we settle it outside the court, then there will be a win-win solution," he added.
Suharto's allies had called earlier in the week for the case to be abandoned but they were rebuffed by the attorney general.
Suharto has rejected allegations he and his family were sitting on a fortune of stolen money.
Investigations into several other charitable foundations that Suharto chaired have been ongoing. It was not immediately clear whether these would continue.
Yudhoyono himself was rushing back to the country on Saturday from Malaysia, where he cut short an official visit by several hours.
Suharto's six children and many of his extended family had gathered at the hospital on Friday night.