At least 67 people were killed by the initial quake in the Pacific nation's mountainous interior on February 26, according to the Red Cross, with 500 injured and 17,000 displaced.
Aid has yet to reach isolated parts of the Southern Highlands, Western, Enga and Hela provinces, with landslides, ruined roads and dozens of aftershocks hampering efforts.
But O'Neill told reporters food, water and medicine was starting to get through, with aircraft ferrying supplies to Moro and Mendi airports in the Southern Highlands.
"Over the last few days, we've been working with the Australian government, with Exxon(Mobil), with Oil Search and Ok Tedi in particular, in making sure that immediate assistance required by the communities is delivered."
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Australia and New Zealand have pledged aid, while Israel has delivered 40 generators to help restore power.
The rugged terrain has made delivering relief supplies difficult with the Red Cross working to reach the Nipa-Kutubu district near the epicentre to assess damage and needs, said the group's PNG secretary general Uvenama Rova.
International Red Cross PNG country head Udaya Regmi added: "We are anxious to reach communities while there is a lull in what is usually a season of heavy rain.
"A big downpour could bring landslides in hillsides already destabilised by the earthquake, cause floods and contaminate water."
Local MP James Marape told The National newspaper there had been more than 50 aftershocks so far, with people too scared to sleep in their homes, fearing they will collapse. Instead they are spending the nights outside.
"The effects of the continual tremors are both physical and psychological," said Marape, speaking from Tari, adding that at least 11 people had died in landslides in the area.
"For the last two nights, I have been witnessing people out in the cold and rain, fearing to go into their houses in case the earthquake strikes again."
Accounts of last week's disaster continue to emerge with local media reporting on a nine-year-old girl, Jerina Peter, who was thrown to safety by her father from a cascading landslide before he was swept away.
Australian officials based in the country have said it was the biggest earthquake to hit the highland region in a century. No official government death toll has been released.
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