"Indonesian-flagged boats with Indonesian crews are breaking our laws bringing people into our territorial waters. This is a breach of our sovereignty," Australia's longest serving foreign minister told Australian Broadcasting Corp. television late Thursday.
"Instead of a lot of pious rhetoric about that Australian government threatening their sovereignty, their people, their boats, their crews are breaching our sovereignty," he added.
Abbott would not comment Friday on Downer's statements and played down the potential impact on bilateral relations of Australia's new border security policy.
Scores of people from war-torn countries use Indonesia as a transit point every year, boarding rickety fishing boats bound for Australia's Christmas Island, located 500 kilometers (310 miles) south of Indonesia's capital, Jakarta.
A boat carrying dozens of asylum seekers sank off the coast of Indonesia's main island of Java on Friday, killing at least 21 people. Survivors said the boat was headed for Christmas Island.
Abbott's government took office last week after a crushing election victory on Sept. 7, partly on a promise to stop the boats full of asylum seekers.
"This is a broad and deep relationship which is going to get broader and deeper over time, and the last thing that anyone should want is to have Australia's relationship with Indonesia defined by this boats issue which I am sure will be but a passing irritant," Abbott told Melbourne Radio 3AW.
Abbott flies to Jakarta on his first international trip as prime minister on Monday and will hold a one-on-one meeting with President Susilo Bambang Yudhoyono. Abbott will be accompanied by Bishop, Trade Minister Andrew Robb and 20 senior business people during the two-day visit, the prime minister's office said in a statement.
The bilateral relationship was one of Australia's most broad-based, spanning business, education, defense, security and people-to-people links. Indonesia is an important commercial partner for Australia, with two-way trade valued at 14.6 billion Australian dollars ($13.6 billion) a year, the statement said.
Abbott has said keeping his government's promise to curb a recent influx of asylum seekers reaching Australian shores by boat is key to its re-election in three years.
The government announced this week that it will not tell the media when boats have been forced back.
Acting opposition leader Chris Bowen said Natalegawa's publicly announcing his concerns about the policy represented a failure by Bishop as foreign minister.
"It takes a special effort to endanger such as important bilateral relationship in the first week of office before Mr. Abbott and President Yudhoyono have even met," Bowen said.
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Associated Press writer Niniek Karmini in Jakarta, Indonesia, contributed to this report.