Anti-corruption bodies will gain new powers under changes to the government’s encryption legislation but Labor will continue to push to improve protections against the creation of “systemic weaknesses”.

On Tuesday the shadow attorney general, Mark Dreyfus, accused the Coalition of welching on a deal to support amendments consistent with a bipartisan security committee report and announced the opposition will push them in the Senate.

Labor will also refer the Telecommunications (Assistance and Access) Act – which grants law enforcement powers to demand tech companies create backdoors in users’ products – to another inquiry to assess its economic impact.

The chair of parliament’s joint intelligence and security committee, Liberal MP Andrew Hastie, announced that Labor and the Coalition had agreed that commonwealth and state anti-corruption bodies should gain the bill’s key powers for law enforcement agencies to compel technical assistance to access electronic communications.

The home affairs department had argued it is “inconsistent” for bodies such as the New South Wales Independent Commission Against Corruption to have powers to intercept electronic messages but prevent them from obtaining technical assistance to read them.

Labor passed the encryption legislation on the final parliamentary sitting day of 2018, withdrawing its amendments in the Senate because it feared failure to pass the bill before Christmas would allow the government to argue it had compromised national security.

It extracted a concession from the government that it would facilitate consideration of the Labor amendments in the new year.

The government leader in the Senate, Mathias Cormann, went further, promising to support “all amendments that are consistent” with the joint parliamentary committee on intelligence and security report under a bipartisan deal reached in early December that almost collapsed hours before the end of the final parliamentary session.

Dreyfus said that the government had “tried to resile from that commitment” and it was “not tenable” to argue that the Coalition had faithfully implemented the committee’s recommendations.

“No reasonable person accepts that,” he said. “The Inspector-General of Intelligence and Security, who made a public submission to the committee, doesn’t accept it.”

Dreyfus said Labor wants to add an amendment so that technology companies cannot be compelled to do anything that would, or could, “compromise the security of the critical systems or result in the personal information of innocent third parties being left vulnerable to hackers”.

He added that “as a matter of principle, Labor does not believe that the attorney general or a senior police officer should be given the power to compel an innocent person, unconnected to an investigation, to provide technical assistance to a government agency without a warrant”.