The confrontation has drawn global attention to Canberra's tough immigration policy, under which asylum-seekers who try to reach Australia by boat are sent to remote Pacific camps on PNG's Manus Island and the island nation of Nauru.
Most of the 600 refugees detained at the camp refused to leave when Australia officially closed it on October 31 after the PNG Supreme Court ruled the site unconstitutional, citing fears for their safety outside.
They are barred from resettling in Australia and Canberra has struggled to transfer them to third countries.
Kurdish-Iranian detainee and journalist Behrouz Boochani told AFP on Tuesday that the detainees were going to dig another well, a day after police moved into the camp to puncture or remove tanks holding the refugees' remaining supplies of drinking water.
"It's the moment to accept failure & let us go to a 3rd country," Boochani, who has acted as a spokesman for the refugees, added in a tweet Tuesday.
Police, who have so far complied with orders from higher authorities not to resort to force to remove the men, used loudspeakers to appeal to the detainees to move on Monday.
Chief Inspector David Yapu issued a statement late Monday indicating growing impatience at the stalemate, after the refugees ignored several deadlines for the camp to be cleared.
"Those refugees were sitting in their compounds and staring at us without any signs of moving out from the centre," the Manus provincial police commander said in the statement.
"Apparently my message went through deaf ears and into the brick wall."
Yapu added that he needed "some clear directives on our next course of action" to persuade the men to leave.
PNG police said they have managed to get about 180 men to voluntarily relocate to three nearby transition centres.
Boochani said those who agreed to move to those new sites have complained about the harsh conditions there.
Canberra has been hopeful that up to 1,250 refugees on Manus and Nauru could be transferred to the United States under a resettlement deal struck last year.
But so far, just 54 refugees have been accepted by Washington, with 24 flown to America in September.
At the same time, Australian Prime Minister Malcolm Turnbull has snubbed an offer from New Zealand to resettle 150 refugees, citing fears it would restart the people-smuggling trade.
His New Zealand counterpart Jacinda Ardern has expressed concerns about Manus and said Saturday she would raise the issue with him at the East Asian Summit in Manila this week.
"In terms of the people currently at the Manus Island centre, they should comply with the lawful requirements of the government of Papua New Guinea," Turnbull told reporters in the Philippines on Tuesday, adding that the US deal "is progressing".
Despite widespread criticism, Canberra has defended its offshore processing policy as stopping deaths at sea after a spate of drownings.
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