"The most regrettable episode in this whole political drama is that no one in the know was able to tell the nation at large the real health status of the Grand Chief," O'Neill was quoted by The National as saying.
O'Neill paid respects to Somare but said his government had become unfocused and complacent on issues of good governance, national wellbeing, and national development in his absence, according to the report.
Somare has undergone multiple surgeries in a Singapore hospital since April, which included a stint in intensive care.
Arthur Somare announced his father's resignation in late June back when he was still the Public Enterprises Minister.
But Sir Michael has not yet announced his own resignation.
While Parliament overwhelmingly voted in O'Neill as his successor early this month, more court challenges over whether this election was constitutional could be on the cards.
Somare made Sam Abal the acting prime minister before he went on medical leave, and Abal's subsequent cabinet reshuffles proved to be costly.