JAKARTA (AFP) - Australian Prime Minister Tony Abbott called the Indonesian president on Tuesday to express regret after axing a trip to Bali reportedly due to fears an asylum boat turn-back could inflame tensions, Jakarta said.

The call came as Indonesian officials said a group of asylum-seekers were discovered on Sunday after being returned by Australian authorities, who used a new tactic by putting two boatloads of would-be refugees into one vessel before escorting them back.

At the weekend Abbott abruptly cancelled the visit to a conference on the resort island of Bali, which had been viewed as a bid to thaw ties damaged by Canberra's border protection policies and a row over spying.

Reports said he axed the trip, during which he had been due to meet Indonesian President Susilo Bambang Yudhoyono, over fears the ongoing boat turn-back could worsen tensions.

But the conservative leader sought to ease tensions over the missed visit on the opening day of the meeting on Tuesday by making a call to Yudhoyono, the president's office said in a statement.

"(Prime minister) Abbott expressed his regret for not being able to accept President Yudhoyono's invitation to attend the Open Government Partnership Asia-Pacific Regional Conference," said the statement.

"The president said he understood the reasons for the (prime minister's) absence which were related to budget talks in parliament".

Yudhoyono and Abbott also welcomed "progress on a code of conduct between the two countries' foreign ministers", said the statement.

It was referring to a code to govern behaviour between the neighbours that Jakarta has demanded following allegations in November that Australian spies sought to tap the phones of Yudhoyono and his inner circle in 2009.

Abbott also said he hoped to visit Indonesia in June as part of an overseas tour, the statement added.

The Australian leader's official reason for not attending the talks was budget deliberations back home although reports say that Canberra was concerned about the ongoing boat turn-back as part of its military-led people-smuggling crackdown.

The Indonesian navy has revealed that it had found a vessel with 19 would-be refugees stranded on Lay island in East Nusa Tenggara province, in eastern Indonesia, early Sunday.

Security ministry spokesman Agus Barnas said the Australian navy found two boats with asylum-seekers that had sailed from Indonesia in their territorial waters late Thursday.

Two Nepalese boatpeople from a smaller vessel were loaded into the second vessel which was then taken back towards Indonesia, he said.

The smaller boat was set on fire, he added.

Abbott's visit to Indonesia would have been his first since the spying revelations emerged and sparked a serious diplomatic crisis between the neighbours.

Jakarta reacted furiously to the news, recalling its ambassador and halting cooperation in key areas including defence and people-smuggling.

Tensions were further inflamed by Canberra's crackdown on asylum-seekers making their way to Australia by boat from Indonesia.

The crackdown, named "Operation Sovereign Borders", involves Australian vessels turning back asylum-seeker boats to Indonesia when it is safe to do so.