Vice President Boediono is only scheduled to meet Deputy Prime Minister Warren Truss.
Deputy Opposition leader Tanya Plibersek says Mr Abbott and Ms Bishop should be taking the opportunity to discuss asylum seeker policy with the Indonesian vice president.
Opposition Immigration spokesman Richard Marles continues to criticise the government's handling of the relationship with Indonesia.
"We have got a government which is engaging in schoolyard diplomacy backed up by half-assed resolve, half-hearted resolve and that is a real mistake for this government."
Earlier, Immigration Minister Scott Morrison says there is "no rhyme or reason" to why Indonesian authorities do not take stricken asylum seekers back to their shores.
"There's no real rhyme or reason to it necessarily," Mr Morrison told Fairfax Radio on Monday. "I think this last instance became very problematic because it became very public."
Mr Morrison says he had given the Indonesian government an undertaking that when such incidents occurred "we would do it directly and we would do it discretely".
An Indonesian MP was reported on the weekend as saying three out of three out of six Australian requests to take back people who'd been rescued had been declined since September.
But the minister said there had only been four such cases.
The Australian Greens say the government has created the problem by not being transparent about its asylum seeker policy, known as Operation Sovereign Borders.
"Mr Abbott's excuses for secrecy are wearing thin and the Greens will use the powers of the parliament to reinforce transparency," Greens immigration spokeswoman Sarah Hanson-Young said.
Opposition frontbencher Penny Wong is calling the situation absurd.
"Australians are looking to the Jakarta Post to get information about what their government is doing," she told the ABC.
"They are a government that does not want to tell Australians what they are doing."
But Mr Morrison says the debate amounts to "hyperventilating" by the government's opponents.
"What they won't acknowledge is we are succeeding - 75 per cent down on arrivals of illegal boats since Operation Sovereign Borders commenced. And our returns overseas have doubled."
The minister says it is also frustrating that Indonesia has no significant search and rescue services based on their southern coastline.
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