His son, Public Enterprises Minister Arthur Somare, recently held a media conference.
"I wish to talk about my old man's health," he said, according to The National newspaper.
"It is ten weeks since he has gone into operation. It has been a challenging period for myself and my family.
"At this time, there is great uncertainty for his recovery."
The 76-year-old first and current PNG prime minister entered Singapore's Raffles Hospital to undergo heart surgery in April.
In the previous month Somare had collapsed at a leadership tribunal appearance. The stress of those proceedings is believed to have contributed to his heart problems.
The National reported that the operation to replace his aortic valve went adequately but the leader subsequently needed two corrective surgeries after his kidneys and lungs started malfunctioning.
A later fungal blood infection only added to these serious conditions.
Arthur Somare told the media conference that the family had been concerned they might lose him.
"That is over now and the kidney is functioning and his health is stabilising," he said, according to The National.
The newspaper said family members wanted Somare to recover in peace without the pressure of making political decisions.
All six direct members of the family are reportedly expected to meet in Singapore next week and make a decision on the leader's future.