Immigration and border protection officials might be hauled back before a Senate committee to face a second grilling about the federal government's crackdown on asylum-seeker boat arrivals.
The Australian Greens are upset officials withheld information about Operation Sovereign Borders during an earlier Senate estimates hearing.
The party seeks Labor support for another hearing.
Greens senator Sarah Hanson-Young said it was absurd to withhold information from Senate estimates on the basis it would be provided at the operation's weekly media briefing.
"Operation Secret Boats is a media strategy and nothing more," she said in a statement.
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Senator Hanson-Young said questions about asylum-seeker boat arrivals that went unanswered included queries about the scope of co-operation with Indonesia.
During the earlier hearing officials from Customs and the Immigration Department and operation commander Lieutenant-General Angus Campbell refused to comment on reports the bow of a rickety asylum-seeker boat was ripped away while being towed near Christmas Island last week.
Passengers are understood to have been thrown into the water.
Lt-Gen Campbell also refused to say how many boats had been turned back to Indonesia since the operation began on September 18.
