Australia is offering Indonesia extra money and help to reduce the number of transiting asylum seekers as the Abbott government maintains silence on the widespread belief that it is towing boats back to the Indonesian maritime border.

At the same time the immigration minister, Scott Morrison, has revealed there is still no agreement about what rights, conditions or assistance will be available to asylum seekers sent by Australia to Manus Island and Nauru who are found to be genuine refugees, even though processing has now resumed at both detention centres.

Indonesian ministers have rejected the policy of towing back or turning back boats, but Morrison sought to smooth the reaction with repeated assurances that Indonesian territorial sovereignty would never be violated and with the offer of increasing Australia’s current $40m contribution to the International Migration Organisation to handle asylum seekers in Indonesia and an open offer of further help, including helping Indonesia send asylum seekers back to their country of origin.

“Australia stands ready to further assist Indonesia to manage this resident population as required or requested … will continue to provide the same level of resettlement [under the humanitarian program] as under the former government, and we are open to assist with voluntary and involuntary returns to assist Indonesia,” he said, pointing to a sharp fall in recent months in the number of asylum seekers arriving in Indonesia.

Morrison said the government was “salvaging resettlement arrangements” for asylum seekers sent to Manus Island, having been left a “blank sheet of paper” by the former government, which began the policy of immediately sending asylum seekers arriving by boat with no possibility of resettlement in Australia shortly before the federal election. The government is building accommodation on both islands to house people found to be refugees.

But asked whether those refugees would have work rights or freedom of movement or family reunion rights, Morrison said “they are matters for the PNG government, there has been no conclusion on those points”. He said discussions were continuing between Australia and PNG.

Morrison and Operation Sovereign Borders commander Lieutenant General Angus Campbell continued to insist that their refusal to answer questions about “on water matters” was essential to meet the overriding goal of stopping asylum seeker boats, and said from now on such briefings on the policy would be held when needed, rather than every week because the “establishment phase” had finished.

They also refused to answer questions about reported attempts at self harm and hunger strikes at the Christmas Island detention centre on the grounds that it could encourage more such protests.

Campbell did confirm reports that the government had bought several large lifeboats – apparently to help transfer asylum seekers back to Indonesia – but would not say what they would be used for.

“I am not going to provide information about the potential or actual employment of these lifeboats now or in the future,” Campbell said, adding “clearly a lifeboat is involved in the on water activities”.

The Indonesian foreign minister, Marty Natalegawa, said sending asylum seekers back in lifeboats was the start of a slippery slope.

"Developments of the type that has been reported in the media, namely the facilitation by way of boats, this is the kind of slippery slope that we have identified in the past," Natalegawa told the ABC.

"It is one thing to turn back the actual boats on which they have been travelling, but another thing to transfer them to another boat."

Morrison has repeatedly pledged that none of the more than 30,000 asylum seekers already in Australia would gain a permanent protection visa, but the Senate has rejected the Coalition’s alternative temporary protection visas and there are three high court challenges under way to the regulations the government is using to prevent permanent visa claims.

Morrison said he would not “speculate” on the outcome of high court cases, but said he “stood by” the commitment that the asylum seekers would not be allowed to stay permanently.

Campbell said allegations of mistreatment by asylum seekers on a boat allegedly towed back to the Indonesian maritime border by the Australian navy had been investigated and he was “very satisfied with the professional conduct of our people”.

He said this did not amount to a confirmation that the towbacks had actually occurred and that the investigation had not included any contact with the asylum seekers, now back in Indonesia, who had made the allegations.

“I just ask that you might reflect on the question of what might be the motivations behind those sort of claims … some of those claims were quite outrageous,” Campbell said.

Morrison said he had “absolute faith in the integrity of our military personnel” and that the claims had been made by asylum seekers at the urging of people smugglers in order to “undermine a policy that is destroying their business”.

He also denied the towback policy broke the government’s promise before the election that it would not tow boats back. He said it had meant the government would not tow boats back to Indonesian ports, not that they wouldn’t be towed at all.

On October 1, at a media conference in Indonesia, Abbott said "can I just scotch this idea that the Coalition's policy is or ever has been towbacks. Our policy ... is that we reserve the right to turn boats around where it is safe to do so. There is a world of difference between turning boats around in Australian waters and the Australian navy towing them back to Indonesia."

But Morrison explained on Wednesday that “previously before the election … the towback as a policy was explained and … was characterised as boats being towed back into Indonesian waters, or into Indonesian ports … we’ve said very plainly it has never been our policy to violate Indonesia’s territorial sovereignty. I think there has been confusion on the semantics of this.”

Both Morrison and Campbell hailed the fact that no boats had arrived for more than three weeks.

"The right policies are in the right hands and they're beginning to get the right results," Morrison said, adding that boat arrivals had fallen 80% since Operation Sovereign Borders began.

Campbell said it would only be able to offer a confident assessment of the success of the operation in March, when the monsoon season was over.

At that point, he said, he might also talk about “past activities” but he would not do that now “lest it offer people smugglers with trend analysis that can be used against us”.