Almost 600,000 are receiving the €350 pandemic social welfare payment.
At a Government briefing on the Covid-19 crisis, it was announced that 591,000 people will receive the payment this week.
Meanwhile, there are a further 347,000 employees availing of the temporary wage subsidy scheme which sees the state cover 70pc of their pay while their employer pays the rest.
More than €556m has been paid to employers since this scheme was introduced, while the €350 pandemic unemployment payment is costing around €206m a week.
The new figures reveal the escalating cost of the national health crisis as unemployment continues to soar.
Department of the Taoiseach assistant secretary general Elizabeth Canavan said the Department of Social Protection and the Revenue Commissioner are working together to establish if there are incidents of people claiming both payments.
Ms Canavan said people should immediately terminate their social welfare payment if they are transferred to the employee wage subsidy scheme.
She said around 2,600 people have not received their payment because they entered an incorrect PPS or IBAN number on their application form.
However, the Department of Social Protection is contacting this group of people to get the correct information.
Separately, Ms Canavan said the Government was “aware of reports on social media” of people saying they are “fed up” of the social distancing restrictions.
She said people are “feeling confined” in their homes and neighbourhoods and are getting frustrated by queuing for groceries. “We know people's patience and resolve is waning,” she added.
“We know that every day we're putting out that call for solidarity and community spirit, as well as personal and collective behavioral change.
“This is what is required of each and every one of us at each step to delay the transmission of Covid-19.
“We know that has not fallen on deaf ears so far. We have complied with the restrictions and have succeeded in reducing the spread of the infection. For now we just need to keep going, as best we can.”