The system, which starts 1 July, replaces the rigid 20 job applications a month requirement that frustrated job seekers and employers for many years.
Others have raised concerns about the increasing use of automation to determine whether jobseekers keep their welfare payments or have them stopped.
The union conducted a snap online survey of 447 jobseekers, which found respondents were most concerned about the automated nature of the new system, worried about their ability to reach 100 points and also about being penalised due to difficulties with the online system.
He acknowledged people who replied to the survey were more likely to already have a negative view of the employment services system.
The Australian Council of Social Service has also warned the requirements are too onerous, and that people with barriers to work, limited digital literacy or poor internet access will experience significant challenges with online reporting. The new system has garnered lukewarm support from employment services providers.
Burke has been silent on the new Points Based Activation System (Pbas) and on Wednesday a spokesperson for the minister again declined to comment.
The Pbas system will come into force when the new Workforce Australia employment services model replaces Jobactive next month.
About half of all jobseekers engage with an online portal, rather than job agencies, which will focus on more disadvantaged unemployed people.
Several critics have already criticised the automated nature of the Australian welfare compliance system used to police whether jobseekers have met their obligations or should have their payments suspended.
People will be spared a payment suspension in their first month using the new system.
