The Senate president, Scott Ryan, has warned the government’s encryption bill would undermine parliamentarians’ ability to keep their work secret from police, due to increased covert surveillance powers.

The Liberal senator’s intervention is a further complication in Scott Morrison and home affairs minister Peter Dutton’s campaign to pass the telecommunications (assistance and access) bill in the final sitting fortnight.

In a surprise late submission published on Thursday afternoon, Ryan told the parliamentary joint committee on intelligence and security that the bill “sits in tension” with work to “properly secure privilege against the exercise of executive investigative powers”.

Ryan noted that currently only Asio can obtain a covert computer access warrant but the bill extends that authority to law enforcement agencies and Border Force, which could then remotely access computers and “account-based data” of people who “may be unaware of the execution of the warrant”.

“I note, and accept, advice that there is nothing in the bill that would abrogate parliamentary privilege.

“However, the main issue with covert access in relation to privilege … is that there would be no opportunity for a parliamentarian who considers that material is protected by privilege to raise such a claim.”

Privilege claims are currently governed by protocols requiring law enforcement agencies to seal material seized in searches until parliament can decide if there is a legitimate case to keep them secret because they relate to the workings of parliament.

Ryan warned that without any notice of covert surveillance, “the parliament has to rely on the agency seeking the warrant, and the authority approving it, to have proper regard to privilege”.

“No one within the parliamentary sphere is empowered to intervene.”

Ryan said the aims of protocols to preserve privilege “are not met in the exercise of these powers”. The bill “extends” these difficulties “at the same time as the privilege committees are seeking to rein them in”.

The Senate president suggested fixing the problem would require “a combination of procedural and legislative action”, such as an amendment “providing that it is not lawful for proceedings in parliament to be seized, accessed, listened to, recorded or observed by use of such powers”.

Morrison and Dutton have invoked the threat of possible terrorist attacks over Christmas to urge the committee to expedite its inquiry to pass the bill.

On Monday Duncan Lewis, the head of Asio, said “without question” the bill is urgent but it was a matter for parliament whether to pass it this fortnight.

The committee has so far refused to change its schedule of hearings, which are due to continue on Friday and Tuesday. It is considering a plan to agree to an interim report recommending the bill be passed but confining new powers to counter-terrorism agencies while the committee considers further safeguards and extension to other law enforcement agencies at a later date.

Ryan acknowledged the timeframe for consideration of the bill may not permit the problem to be addressed, and suggested an agreement to fix it in future.

He said he had informed the attorney general, Christian Porter, and Dutton and suggested the committee work with them to protect privileged information.

The government’s telecommunications assistance and access bill, first unveiled in August, contains powers to require tech companies to build new capabilities or provide technical assistance to law enforcement agencies’ surveillance activities, such as breaking encryption.

In a supplementary submission, Digi – the peak body representing tech giants including Amazon, Facebook, Google and Twitter – warned the committee it is not possible to mandate technology providers implement a way to unencrypt data without creating a vulnerability.

Digi has recommended the bill be amended so technology providers cannot be asked to build vulnerabilities or weaknesses into their products or services or impose an obligation to retain data.