The Pandemic Unemployment Payment and the wage subsidy scheme have been extended until the end of August but there will be two levels of PUP payment from 29 June.
Those whose prior earnings were above €200 will continue to get €350 per week but those below €199.99 per week, will get a PUP of €203 per week.
A quarter of those receiving the €350 weekly Covid PUP are to have their benefit cut to €203 per week under reforms.
The move will hit part-time and lower paid workers who were earning less than €200 per week prior to the Covid-19 emergency in March.
At the peak of the Covid crisis, 600,000 people were dependent on the Pandemic Unemployment Payment, but the scheme had anomalies.
Some lower paid workers, including part timers and students, received more on the flat rate €350 Covid welfare payment than they had earned in their pre-crisis jobs.
From the first week of July, those who were earning more than €200 a week before the shutdown will see no change in their Covid payment.
However, those earning under €200 pre-crisis, which is around a quarter of Covid recipients, will have their benefit cut to the standard Jobseekers rate of €203 per week.
Minister for Social Protection Regina Doherty described changes to the payment as the "gentle recalibration" so that it is tailored and more equitable.
A new banded approach to the PUP will ensure it is fairer, she said, and part-time workers will still receive more than they did before the pandemic.
Ms Doherty said she has tasked her department with looking at any future changes to the scheme.
Ms Doherty said nobody's money is being cut and that if we had had the time and the space we would have had a banded Wage Subsidy Scheme or something more staggered.
She said people who are over 66 who may have missed out on any payments are advised to ask the department for help - and the reason they may have missed out is due to the current legislation governing working years.
Ms Doherty said nearly 6,000 students went back to work this week and jobs are opening back up, while Minister for Finance Paschal Donohoe said over 30,000 workers left the PUP scheme and people are going back to work, because of the reopening of the economy.
He said in advance of the end of August, the government of the day will announce how the scheme will be amended and how it can become more viable.
Mr Donohoe said the changes to the structure of the PUP means that it "continues to be a strong support but also a fairer and more targeted support" and is "one further step along the way to re-opening our society.
He said he has asked his department to start working on options for any future changes to the scheme "taking into account progress in the reopening of society and the developing health situation".
Reporting: Maggie Doyle and Sandra Hurley