Senator Hanson-Young said it was unacceptable that the minister had thumbed his nose at the Senate and that General Campbell had refused to divulge key aspects of the taxpayer-funded border protection regime when asked by a properly constituted parliamentary committee designed to examine precisely such information.

It comes as the federal government maintains a high degree of secrecy, claiming that to report on maritime arrivals, interceptions and rescues amounts to a ''shipping news service for people-smugglers''.

The requests will be the subject of tactical consideration at shadow cabinet when MPs return to Canberra next week.

The Greens believe the ban could frustrate a future bill to appropriate funds to establish the headquarters of Operation Sovereign Borders, as well as any subsequent legislation.

''This is no minor matter,'' Senator Hanson-Young said. ''It's a big deal to say that an entire government program is effectively off limits and cannot be held accountable to the Parliament.''

But while Mr Morrison appears to be softening his style after attracting criticism, even within the Coalition, for seeming arrogant, he shows no signs of providing more information.

Speaking on Sydney radio on Monday he said the government ''will not give an inch''.

''Let me liken it to this,'' he said. ''If there was a police investigation under way into a criminal activity up in Brisbane today and it had been going on for several months, you wouldn't expect the police to be turning up every day and giving real-time reports on the latest warrant they served or the latest inspection they undertook or frisk they did or operation they did last night … We're tracking down criminal people smugglers here. And that's no different to trying to stop drugs coming into the country or police trying to stop paedophilia.

''But the Labor Party's call, together with the Greens, they're acting in concert here, for us to provide tactical information about how things are done at sea, we've had Angus Houston, the former chief of [the] defence force say that's not a good idea.''