The federal government is trumpeting the importance of downloading the COVIDSafe tracing app, saying it is crucial to reviving businesses and returning to normal life, but at least three of its own MPs have not downloaded it.

The ABC has checked whether every MP and senator in Parliament has downloaded the app, either by contacting them directly or checking the public record for definitive statements on the matter, ahead of restrictions potentially being lifted tomorrow.

The government has flagged the number of app downloads as a critical factor influencing how quickly those restrictions are lifted

But that has not been enough to convince all of those in Parliament, with at least one member of every party choosing not to download COVIDSafe.

That includes government MPs Barnaby Joyce and Llew O’Brien and Senator Concetta Fierravanti-Wells.

Several MPs and senators, including frontbenchers Michaelia Cash, Dan Tehan and Trevor Evans, did not respond to the ABC’s requests for clarification of their positions, while former cabinet minister Bridget McKenzie declined to comment.

The members of One Nation and the Greens don’t agree on many things, but both parties have expressed scepticism over the app, in contrast to the large majority of Coalition and Labor members who confirmed they had downloaded it.

All Greens MPs and senators have held off on downloading the app apart from South Australia’s Sarah Hanson-Young, with party members citing a distrust of the government’s record on data security.

Some have said they would reconsider downloading the app after further protections passed through the Parliament.

Currently, rules that only allow contact tracers to access data from the app are enforced by a ministerial declaration made by Health Minister Greg Hunt, however draft legislation has been released by the government as MPs prepare to return to Parliament next week.

The draft legislation would impose jail time and fines on anyone found to have collected or disclosed data from the COVIDSafe app illegally.

A distrust of the government was also cited by One Nation senators Pauline Hanson and Malcolm Roberts and Lower House independent Bob Katter, however all were more definitive in their positions that they would not download the app.

Centre Alliance senator Rex Patrick cited confidential meetings he held with whistleblowers as reason not to want his face-to-face contacts recorded, but said he would reconsider his position once legislation passes Parliament.

Of the handful of Labor MPs yet to install COVIDSafe, most said they intended to do so, but only once they were satisfied with the privacy protections on offer.

That’s with the exception of Labor Senator Patrick Dodson, who lives in remote Western Australia and says he intends to install it next time he’s in Broome, the nearest town with stable reception.

Mr O’Brien, a Coalition backbencher, also said he would reconsider downloading the app in light of the government’s legislation.

Many MPs and senators also raised feedback on the app they had received from voters.

While some MPs said they had received either no or only positive feedback, two clear concerns emerged: privacy concerns and phone compatibility.

Many representatives said people had contacted them to say they were concerned their private information would not be kept safe, or to say they wanted to download the app but were not able to because of the make or model of their phone.

More than 5.1 million Australians have downloaded the app since it launched on April 26.

Note: David Coleman and Alex Gallacher are excluded below as they are on personal and medical leave respectively and were not able to provide answers. Outgoing Eden-Monaro MP Mike Kelly has been excluded as he has resigned from Parliament.