Indonesian Foreign Minister Marty Natalegawa described the plans as a breach of his nation's sovereignty that could damage relations between the two countries.
But Foreign Minister Julie Bishop told Sky News: "We're not asking for Indonesia's permission. We're asking for their understanding."
Abbott, while adamant his plans will go ahead, has been more conciliatory. He has spoken to Indonesian President Susilo Bambang Yudhoyono and hopes to visit him in Jakarta ahead of bilateral talks at the Apec summit in Bali next month.
Abbott has also discussed his policies with PNG Prime Minister Peter O'Neill and Sri Lankan President Mahinda Rajapaksa. Sri Lanka is a major source of asylum seekers.
"By virtue of its size, proximity and potential, [Indonesia] is an extraordinarily important relationship to Australia," he said.
But he said he was determined his new measures would go ahead: "I am absolutely determined to stop the boats as quickly as we humanly can.
"This is one of those stand or fall issues. We will make a difference and we will start from day one."
Monitoring the effectiveness of the Operation Sovereign Borders will, however, become more difficult. Unlike its Labor predecessor, the new Government will not release information about the interception of boats.
Instead, it will be treated as an "operational decision" by the commander of the new taskforce, which will bring together the operations of 12 agencies. The commander, a three-star general outranked only by the Defence Force Chief, will report directly to Morrison.
The interception of asylum seekers is mainly tasked to air force Orion aircraft, navy patrol boats, and the customs' fleet of eight ageing patrol boats armed with 7.72 calibre machineguns but Abbott intends leasing extra vessels and to harden the navy's handling of asylum seeker boats.
Although under his policies the cost of measures could rise above the existing annual bill of A$2-A$3 billion a year, he says he will succeed.
The new measures have been attacked by the United Nations, the Human Rights Commissioner, and legal, refugee and human rights organisations.
But Abbott intends to add even tougher moves, including denial of judicial review of refugee decisions, the axing of taxpayer-funded legal advice, and the reintroduction of temporary protection visas for those accepted as refugees. Under the visa scheme these refugees will be denied permanent residency and every three years must prove they face likely persecution if they are returned to their own countries.
