Treasurer Josh Frydenberg introduced the bill on Wednesday, with the extension to cost about $15 billion.
It takes the total cost of the program to more than $100 billion.
JobKeeper will be split into two tiers, resulting in different pay rates for full-time and part-time staff.
Rates will also be staggered down through to March 2021.
“The phasing down of the JobKeeper payment will ensure a smooth and gradual transition to economic recovery, while ensuring that those who most need support continue to receive it,” Frydenberg told parliament.
“The introduction of a two-tier payment rate will also better align the JobKeeper payment with the pre-COVID incomes of recipients, particularly those who worked part-time hours.”
Shadow treasurer Jim Chalmers is worried scores of workers still can’t qualify for the scheme, such as casuals and university and aviation staff.
The rate of the scheme is up to Mr Frydenberg and Labor hopes he aligns the payments with the current state of the economy.
“The ball is now in the treasurer’s court to set the rates and eligibility. We need him to get that right,” Chalmers told parliament.
“If he continues to get that wrong the unemployment queues will be longer than they need to be and that will make it harder for people to put food on the table, put school shoes on the kids and pay their rent or mortgage.”
A review of the initial laws found anomalies in the way it operated.
Labor is supporting the legislation even though the party’s concerns about employers cutting working hours aren’t addressed.
Firms remaining on JobKeeper will still have the power to change employees’ hours, duties or work location.
Others booted off JobKeeper will also retain the capacity to change conditions if they prove a 10 per cent reduction in turnover.
The Morrison government plans to cut the wage subsidy from $1500 to $1200 a fortnight at the end of September and then to $1000 from December to March.
Labor wants JobKeeper to remain at $1500 a fortnight for another six months, with Victoria’s coronavirus lockdown smashing the national economy.
Meanwhile, workers in Tasmania will receive access to $1500 a fortnight pandemic leave payments after the state and federal governments struck a deal.
The payments are designed to support workers with no sick leave through their 14-day coronavirus self-isolation period.
-AAP
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