Australia's spy chief has called for legislation allowing law enforcement agencies easier access to encrypted messages to be passed as quickly as possible.

Duncan Lewis has told a parliamentary committee there is "without question" an operational urgency to enacting the decryption laws due to a worsening "capability gap".

"I anticipate ASIO would immediately use this legislation if and when it becomes available," he told committee members in Canberra on Monday.

"ASIO has cases afoot at the moment where this legislation will directly assist."

The federal government wants the intelligence and security committee to speed up its public hearings so the laws can be passed before Christmas.

Mr Lewis said Christmas was generally a high point for terror threats, but the spy agency had no evidence of a specific attack being planned for a particular time or place in the upcoming holiday season.

He said while the new decryption powers would be beneficial, whether the legislation was passed before Christmas or after was a matter for the parliament and the government to decide.

"I really don't have a position on that," he said.

Technology giants including Twitter, Facebook and Google have raised serious concerns about the scope of the bill and a lack of oversight.

The companies are concerned the proposed powers could erode customer trust and undermine public safety by making it easier for "bad actors" to commit crimes against individuals and organisations.

But Mr Lewis said the powers would help enormously in tackling not just terrorism but also foreign espionage and organised crime.

Victoria Police Assistant Commissioner Neil Paterson said almost all would-be terrorists and perpetrators of serious and organised crimes were using encrypted messaging.

"At the moment, we're fighting with one hand tied behind our back by not being able to lawfully access the data we need to," he told the committee.

Home Affairs Minister Peter Dutton has urged the committee to accelerate its deliberations.

"The situation has become more urgent in light of the recent fatal terrorist attack in Melbourne and the subsequent disruption of alleged planning for a mass casualty attack by three individuals," Mr Dutton wrote to the committee.

"I am gravely concerned that our agencies cannot rule out the possibility that others may also have been inspired by events in Melbourne to plan and execute attacks."

Shadow attorney-general Mark Dreyfus said the government had pinned its request to accelerate the hearings on the possibility of potential terror attacks.

Mr Dreyfus asked for a view on whether agencies with counter-terror functions should be given the new powers in the short term, but not other agencies such as anti-corruption bodies.

Home Affairs secretary Michael Pezzullo said the change would require amendments to carve out certain agencies.

"If that's what committee decides ... it's certainly not a complex drafting change," Mr Pezzullo said.

Two more public hearings are scheduled for later this week, with federal politicians in Canberra for the final sitting fortnight this year.