Attorney-General George Brandis has sought to quell free speech concerns about the government's national security reforms by giving himself the power to veto prosecutions of journalists who publish details of undercover ASIO operations.

The decision follows a growing backlash against a law passed more than a month ago that includes jail terms of up to 10 years for anyone who discloses details about ASIO "special operations", during which the security agency's officers would have partial legal immunity in the event they have to break the law in the course of their work.

Amid concerns that the law could prevent journalists reporting on, say, botched special operations, Opposition Leader Bill Shorten wrote to Prime Minister Tony Abbott on Thursday asking that an independent watchdog on national security laws review the clause by the middle of next year.

Senator Brandis said it was highly unlikely a journalist would ever be targeted for doing his or her job.

But to assuage "false" concerns about journalists, he would use his existing powers to direct the Commonwealth Director of Public Prosecutions against launching action against a member of the media that he considered to be inappropriate.

That would mean any Attorney-General would, as an elected politician, have to "take personal and therefore political responsible for any prosecution were any ever to be considered".

"That would mean that in the barely foreseeable, barely imaginable event that a journalist were the subject of a prosecution brief to the Commonwealth DPP, the Attorney-General, as a political official, as a minister, would assume immediate responsibility for allowing that prosecution to proceed," he said.

He described that as a "powerful safeguard" but admitted future attorneys-general would not necessarily have to adhere to the same principle and could in fact even revoke vetos that Senator Brandis himself had placed on prosecutions.

He also stressed that he could not direct the DPP to launch a prosecution that wasn't already being considered.

The law was not aimed at journalists but was for "general application" in fact was "primarily … intended to deal with a Snowden-type situation", Senator Brandis said, referring to the massive intelligence breach perpetrated by the renegade US intelligence contractor Edward Snowden.

Senator Brandis has described Snowden as a "traitor" who put Australian lives at risk by leaking confidential surveillance documents.

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