John Howard' statement was seen as an attempt to calm tensions between Australia and Indonesia after a family of six attempted to flee the troubled province by boat.
The family would have become the first asylum seekers from Papua, also known as West Papua, to arrive in Australia since 42 Papuans were granted asylum last month.
That incident caused a backlash from Indonesia, which accused the Australian government of intervening in its affairs. It denied allegations of genocide in the province and recalled its ambassador to Canberra.
With anti-Australia feeling on the rise in Indonesia, on Thursday an Indonesian trade group called for a boycott of Australian goods.
Commenting on the asylum case, Howard said he welcomed news that the Papuan family had, contrary to reports on Wednesday, not made it to Australian shores.
"I would say to people in West Papua and I would say to any people in Australia ... who may be encouraging them to come to Australia that that is not something that the Australian government or, I believe, the majority of the Australian public wants"
Australian prime minister
Later reports said the family's boat had run short of fuel and diverted to Papua New Guinea, a country that shares an island with the province.
"The original reports that they had come to an island off the Australian coast are now seen as wrong," Howard told ABC radio on Thursday.
"That is a good thing in the context of the relationship between Australia and Indonesia."
Howard said that relations between the two had come "under strain" because of this issue.
"I would say to people in West Papua and I would say to any people in Australia ... who may be encouraging them to come to Australia that that is not something that the Australian government or, I believe, the majority of the Australian public wants."
Amanda Vanstone, the Australian immigration minister, warned would-be refugees that Canberra's decision to grant asylum to the 42 who arrived in canoes from Papua in January did not mean that other Papuans would succeed.
Vanstone said refugee applications were decided by her department on a case-by-case basis and did not reflect a judgment on the Indonesian government.
"Each of these decisions are made individually ... that is, what was happening to them and their fear in a particular area," Vanstone told ABC radio.