Relations between Australia and Indonesia tumbled in late November after Jakarta said it was suspending military and intelligence cooperation, including joint anti-people smuggling activities, over Australia's alleged spying activities.
Indonesia recalled its envoy after leaked documents indicated Australia tried to spy on senior government politicians, including wiretapping the cell phones of President Susilo Bambang Yudhoyono and members of his inner circle.
Abbott said Indonesia's actions have been ''unhelpful'' and the tide of asylum seekers arriving in Australian waters continues, The Age newspaper reported.
''There's no doubt that the suspension of co-operation by the Indonesian authorities has been unhelpful,'' he said at a news conference marking 100 days since his Liberal Party coalition government took office.
"Given that people-smuggling is a crime in Indonesia, just as it's a crime in Australia, I think it's high time that that co-operation was resumed.''
The diplomatic damage was inflicted after documents obtained by the Australian Broadcasting Corp. and The Guardian-Australia indicated Australian intelligence had attempted to listen to the president's phone conversations at least once.
Also targeted were the phone conversations of his wife, Ani Yudhoyono, and other senior Indonesian government members, ABC reported at the time.
Intelligence officials also tracked activity on Yudhoyono's cell phone for 15 days in August 2009, documents indicated.
The Age reported that an asylum-seeker boat reportedly carrying about 70 people arrived last week, bringing to seven the number of vessel arrivals since Jakarta halted cooperation Nov. 20.
An undercover investigation by Fairfax Media suggested people smugglers are taking advantage of the rift in relations.
The Age, part of Fairfax Media, reported that in a secretly recorded conversation with a prospective customer, a prominent people smuggler specifically referred to the deteriorating relations in his sales pitch.
"We are certainly being as good a friend as we humanly can to Indonesia," Abbott told ABC's Radio National.
"I think it would be the act of a good friend to swiftly resume anti-people smuggling co-operation."
Abbott said he hoped co-operation would resume "well before" July when President Yudhoyono's term ends.
Abbott also announced that he has disbanded the Immigration Health Advisory Group that provided advice to the government on the physical and mental health of immigration detainees. The group consisted of nine experts, including psychiatrists, psychologists, nurses and general practitioners.
The Australian newspaper reported that members of the group were told on Friday that its chairman, Maj. Gen. Paul Alexander, a medical doctor with the Australian Defense Force, is being kept on to provide the same service to the Department of Immigration.
"It's just that we've moved from an unwieldy committee to a single officer,'' Abbott said.
Amanda Gordon, who represented the Australian Psychological Society in the group, told World News Australia Radio that members had no warning of the disbanding.
The Australian Green Party said the move was "short-sighted and cruel" and the opposition Labor Party called the axing "appalling."
Australia's federal election in September saw both the governing Labor Party and opposition Liberals saying they would get tougher with people smugglers and put an end to a decade-long influx of asylum seekers arriving by boat.
Abbott, immediately upon taking office, set up Operation Sovereign Borders -- an amalgamation of Australia's 12 agencies involved in border protection under the command of a single three-star military commander.
An investigative report in the Sydney Morning Herald in October found 1,500 asylum seekers have died trying to reach Australia since 1989.
The worst disaster was in October 2001 when the SIEV X sank, drowning 146 children, 142 women and 65 men, the Herald reported.