Senior ministers and top bureaucrats have denied the government wants to give the nation’s military spy agency unprecedented powers to monitor Australian citizens.

News Corp reported on Sunday that the heads of the Home Affairs and Defence departments had exchanged letters on a proposal to boost the powers of the Australian Signals Directorate (ASD).

Under the proposal, the ASD would for the first time be able to access Australians’ emails, bank records and text messages – a proposition Labor described on Sunday as a “power grab” by Peter Dutton.

Currently the ASD only collects intelligence on foreigners. Its motto is: “Reveal their secrets, protect our own”. It is perhaps best known for allegedly bugging the phone of Indonesian president Susilo Bambang Yudhoyono.

The Labor opposition claimed the leak must have come from within the government.

Foreign Minister Julie Bishop said there was “no plan” to expand the ASD’s powers, adding she could not see a “national security gap” that would justify such a proposal.

“There is no plan for the government to extend the powers of the Australian Signals Directorate so that it could collect intelligence against Australians, or covertly access private data,” Ms Bishop said.

“There is no such plan.

“I don’t see any national security gap, and I certainly believe the current laws safeguard the privacy of Australians but also keep Australians safe.”

According to News Corp, Home Affairs Secretary Mike Pezzullo wrote to Defence Secretary Greg Moriarty to outline a plan that would “proactively disrupt and covertly remove” onshore cyber threats by “hacking into critical ­infrastructure”.

In a joint statement, Defence, Home Affairs and the ASD said there was “no proposal to increase the ASD’s powers to collect intelligence on Australians or to covertly access their private data”.

They said the ASD’s cyber security function was being “enhanced under reforms agreed by the government last year”.

“The cyber security function entails protecting Australians from cyber-enabled crime and cyber-attacks, and not collecting intelligence on Australians. These are two distinct functions, technically and operationally.

“In the ever-changing world of cyber security, as officials we should explore all options to protect Australians and the Australian economy.

“We would never provide advice to government suggesting that ASD be allowed to have unchecked data collection on Australians – this can only ever occur within the law, and under very limited and controlled circumstances.”

Current laws prohibit the ASD from spying on Australian citizens. ASIO and the AFP have those powers but must obtain a warrant issued by the Attorney-General.

Under the new plan, approval for the ASD to spy on Australians would instead be given by Defence Minister Marise Payne and Home Affairs Minister Peter Dutton.

“The Department of Home Affairs advises that it is briefing the Minister for Home Affairs to write to you [Ms Payne] seeking your support for a further tranche of legislative reform to enable ASD to better support a range of Home Affairs priorities,” according to a ministerial submission reported by News Corp.

Mr Dutton was yet to write to Ms Payne about the proposal, News Corp said.

Labor’s defence spokesman Richard Marles said the ASD needed to be “seen as an asset of Defence” not Mr Dutton’s Home Affairs department. 

“When you are talking about the surveillance of Australians – which occurs now through the police, through ASIO – there’s a whole legal apparatus around that, providing safeguards, the requirement of warrants,” Mr Marles told the ABC’s Insiders program.  

He claimed the proposal appeared to be a power grab from Mr Dutton.

“We need to be clear here, our nation’s security and an accumulation of Peter Dutton’s power are two different things,” he said.

“It concerns me that at times the government confuses them.” 

Deputy Labor leader Tanya Plibersek said the leak was highly classified.

“Who is it in government that is leaking highly classified information — perhaps to try and stop Peter Dutton’s latest power grab?”