This comes as an Indonesian MP said a visit to Jakarta by Australia's most senior diplomat will fail without ministerial representation.
The visa issue has sent relations between the two countries plunging to their lowest point since the East Timor crisis in 1999.
The head of the Department of Foreign Affairs and Trade, Michael L'Estrange, will head to the Indonesian capital for meetings with ministers and senior advisors to try to soothe the row.
But outspoken nationalist MP Djoko Susilo, a member of the Indonesian parliament's powerful foreign affairs commission, said Australia should instead be sending a senior minister.
"I regret that the government of Australia did not send a decision-maker person like Alexander Downer or Amanda Vanstone, the Minister of Immigration herself," he told ABC Radio.
"I think the trip, which is intended to heal the rift ... will not succeed."
No apology
But Mr Howard has insisted that Australia does not need to apologise.
"This is a difficult issue," he told Southern Cross Broadcasting in Perth.
"It's not an insurmountable problem, it's not an insoluble one, I'm sure we can work our way through it but it will take time."
He said it is sensible to first have Mr L'Estrange to speak with the Indonesians.
"After that I'm sure there'll be contact between the foreign ministers and then at some time after that I'm sure there'll be contact between the President and myself," he said.
Indonesian President Susilo Bambang Yudhoyono on Monday repeated that Jakarta would press ahead with a review of relations with Australia, saying Indonesia cannot be "harassed" and would not be "deprived of fairness".
Indonesia insists that Canberra had no reason to grant temporary visas to 42 of 43 Papuan separatists who landed in Cape York in January, claiming to be victims of human rights abuses.
The decision prompted Jakarta to withdraw its ambassador in Canberra, bringing relations to their lowest point since the 1999 Australian-led military intervention in East Timor.
The Australian government has since moved to toughen its asylum seeker policy, insisting that anyone wanting to enter Australia as a refugee be taken to offshore detention centres for processing.
The move has prompted criticism that it is an attempt to hose down the dispute with Indonesia.
Australia is also increasing naval and customs patrols of its northern coastline to deter more asylum seeker arrivals from Papua, where separatists have waged a low-level battle for independence against Jakarta-rule since the 1960s.