Indonesia's Foreign Minister Retno Marsudi considers Julie Bishop one of the ministers she is closest to, but they don't necessarily communicate through the media, her spokesman says.
Indonesian Foreign Ministry spokesman Arrmanatha Nasir doesn't agree with the previous minister Marty Natalegawa's assessment that communication between the two countries has diminished with recent tensions.
"The Australian foreign minister is one of the closest with our foreign minister," he told reporters in Jakarta on Thursday.
Mr Nasir said the ministers had maintained a good relationship despite recent differences between the neighbours over the executions of two Australians and asylum-seeker boat policy.
"Both of them are women in a very tough global political arena, since the very beginning they have been communicating ... and it's still going on," he said.
At the ministerial level, Australia had sent condolences after Indonesia's military plane crash in Sumatra this week, and remained engaged at lower levels of government, too.
The dialogue wasn't always done in public, Mr Nasir said.
"Is it necessary that every time we have communication, we report it to the media?" he said.
He did not agree with the pessimistic view of Dr Natalegawa, who this week said the nations were at a "critical juncture".
"In a relationship, there's certainly ups and downs, that's a common dynamic," he said.
"We can't say it's at the lowest or not.
"The most important thing is the communication is still going on, it's running well.
"The co-operation in programs is also working.
"The most important thing is that there's good intentions from Australia and Indonesia to keep trying, improving, maintaining relations."
Mr Nasir believed the ministers' next meeting would be the East Asia Summit, due to be held in Malaysia in November.
Ms Bishop, too, disagreed with Dr Natalegawa's criticism, arguing communication was at an "all-time high".
However, Ms Bishop's response to Ms Retno's request for more information on claims a boat crew was paid to return to Indonesia last month did not contain a full explanation, according to Indonesia's ministry.
In March, Jakarta responded tersely when correspondence from Ms Bishop urging a stay of execution for Andrew Chan and Myuran Sukumaran went public.
The letter, which began "My dear Retno", offered to pay costs for the men to remain in prison for life.
At the time, Mr Nasir accused Australia of "diplomacy by media".
Indonesia executed the men in April despite the diplomatic efforts.
