Senior navy officers and government officials may be hauled before a Senate inquiry into how vessels breached Indonesian territorial waters during Operation Sovereign Borders.
The Australian Greens will give notice on Tuesday of a motion to set up a new inquiry.
It will seek information on what operations - such as towing or turning back asylum-seeker boats - were under way when the breaches occurred.
It will also seek answers on whether the operations and procedures of Operation Sovereign Borders breach international law.
The Greens will need the support of Labor to initiate the inquiry.
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Greens senator Sarah Hanson-Young says the government's obsession with secrecy is tarnishing the navy's reputation.
"The Greens' inquiry, which we are giving notice of today, is needed to defend the integrity of the brave men and women who serve in the Australian Navy," Senator Hanson-Young said.
"These incursions are very serious and Tony Abbott's explanations to this point have been woefully inadequate."
Mr Abbott has confirmed that on a number of occasions since the stop-the-boats operation began Australian vessels had accidentally gone into Indonesian waters.
Customs and Defence are currently considering a draft internal report on how the breaches occurred and procedures to ensure they do not happen again.
