It has been six years since the Rudd government announced asylum seekers who arrived by boat would never be allowed to be resettled in Australia and instead processed in offshore detention centres.
"I've met Immigration Minister Peter Dutton already; I've asked him to expedite the processing of asylum seekers," Mr Marape said.
"We need to establish a timeline going forward."
Around 450 asylum seekers remain in PNG and another 350 are being held on Nauru.
"There are genuine refugees and there are also non-genuine refugees. What happens to the rest of them we have in (our) country?" Mr Marape said.
"These are human beings we're dealing with. We can't leave them all hanging in space with no serious consideration into their future."
Greens Senator Nick McKim is being deported from Manus Island on Friday after being denied entry to an asylum seeker processing centre.
"Just had a visit from two Immigration Department officials and been instructed to leave PNG," he tweeted overnight.
"I will accept this deportation and leave Manus tomorrow.
"But no matter where I am I will never stop fighting to expose the truth about the humanitarian calamity of offshore detention."
Amnesty International has used the six-year anniversary to renew its demands to end offshore processing.
"There must be an urgent plan to resolve the situation for all refugees and people seeking asylum on Manus Island and Nauru," Amnesty's Graham Thom told AAP.
"Authorities in Australia should do the only humane thing and immediately bring the refugees and people seeking asylum to safety. The abhorrent practice of offshore detention must end."