The Department of Social Protection has advised employers facing difficulties in re-hiring staff to contact it so that it can "follow up" with the workers concerned.
The advice comes as the latest Department figures reveal that the number of people claiming the Pandemic Unemployment Payment this week has dropped to 376,600.
This marked a decrease of more than 8,500 over the last seven days.
The PUP figures do not include a further 178,000 people recorded on the Live Register as of the end of April.
The Department said it noted concerns expressed in recent days regarding employers facing difficulties in re-hiring staff.
It cited experience from last year showing that around 400,000 people had closed their PUP claims once the economy partially reopened.
"This is clear evidence that the vast majority of people want to, and will take up employment, once it is available to them," it stated.
However, it went on to say that any employer facing difficulties in re-hiring staff can notify the Department at C19employerreports@welfare.ie, adding: "...and we will follow-up with the workers concerned."
The Department noted that throughout the PUP scheme, it has been carrying out control checks and inspections.
This week's PUP payments will cost €111.5m.
12,245 people closed their PUP accounts to return to work, reflecting the gradual reopening of the economy.
Social Protection Minister Heather Humphreys described this week's reopening as a "big step forward" resulting in more people going back to work.
Meanwhile, the Chief Executive of the Restaurants Association of Ireland has called for a clampdown on welfare payments for people refusing to return to an available job.
Adrian Cummins was speaking as the Department of Social Protection announced that employers facing re-hiring difficulties could contact it, and that it will then "follow up" with employees.
Mr Cummins said 30% of hospitality staff were known to have moved to jobs in other sectors - while the remaining 70% were mainly receiving the Pandemic Unemployment Payment or Employment Wage Subsidy Scheme supports.
He said that where positions are available, hospitality employers want people to come back to work and resume gainful employment.
"If they don't, there has to be some mechanism where the Department of Social Protection steps in and deals with it on a case by case basis," he said.
He acknowledged that some business would not be opening for months, citing music, events and night club activity.
However, he said they could not have a situation where employees were refusing to come back to an availalbe job.
"We would welcome a Department clampdown. It's a Department issue so they need to deal with it and advise employers as to how they can forward on details of employees that are refusing to come off PUP even though a job is available for them, " he said.
The small business group ISME confirmed the re-hiring issue was a problem in a number of sectors.
Chief Executive Neil McDonnell said the difficulty arose where people might be getting €250 on PUP for doing nothing, compared to getting €300 for working.
He acknowledged that some employers were asking people to come back, but not necessarily for full hours.