A spokesman for the Royal Papua New Guinea Police Constabulary said the force's hierarchy was deciding what to do with the O'Neill Parliament's order.
"It is something we are considering in-house," the spokesman told AAP. "All options are being considered."
The force currently has two police commissioners - Tom Kulunga, appointed by O'Neill, and Fred Yakasa, who was reappointed by Somare on Monday night.
The police force has stressed that its role is to maintain law and order.
There is a small contingent of police officers loyal to the Somare camp.
In Parliament, O'Neill's manager of government business moved several motions banning Somare and his Cabinet from saying they are the government.
The MPs passed a resolution requiring the Governor-General to attend Parliament to swear in O'Neill.
There were about 50 MPs supporting O'Neill in Parliament yesterday, including Speaker Jeffery Nape.
Somare's supporters were holed up at Port Moresby's Ela Beach Hotel, where they have held Cabinet meetings since Monday.
Meanwhile, PNG's defence force chief has dismissed rumours of a possible military coup.
"The defence force neither seeks, nor would accept, any part to play in the politics of this country," defence force chief Brigadier General Francis Agwi told the Post-Courier newspaper.
"The PNGDF has no political position and takes no political sides," he said.
In Australia, Defence Minister Stephen Smith said there was no reason for the Australian armed forces to get involved.
"We want to see these matters resolved in accordance with PNG's constitution," he said.
PNG's political crisis erupted on Monday when the Supreme Court ruled that O'Neill's August election was unconstitutional and Somare should be reinstated as Prime Minister.
The decision triggered a stand-off on Tuesday, when MPs loyal to O'Neill stormed past armed guards at the gates of Government House following an announcement by Somare's camp that the political veteran was about to be sworn in.
Demanding an audience with the Governor-General, the MPs burst through a blockade of police armed with machineguns and waited at the gate until O'Neill was granted an audience.
Following that meeting, the Governor-General told O'Neill he would make his decision on the prime ministership in writing.
- AAP