The Irish Nurses and Midwives Organisation has described today's meeting with Minister for Health Simon Harris as "positive" and Mr Harris said it was very constructive.
An INMO spokesperson said the main agenda item was the high rate of healthcare workers infected with Covid-19.
The union said the number is unacceptably high at 7,968. There have also been seven deaths among health sector staff.
The INMO wants a rapid independent inquiry into what caused the high rates and how to eliminate the problem.
The spokesperson noted that the union had been seeking detailed statistics on those cases in order to prevent further virus transmission and he said, the minister had agreed to arrange a meeting between the INMO and the Health Protection Surveillance Centre this week to share those figures.
The spokesperson said the INMO would examine them closely and see how best to proceed.
He confirmed that there was also discussion on how the health service could resume non-Covid activities, while the importance of resolving childcare isseus was also raised.
In a statement, Mr Harris said there was a need for more data in relation to Covid-19 and health staff. He said the INMO is to meet the HPSC this week to discuss matters and he confirmed he will meet again with the INMO next week.
Childcare provision, bed occupancy and safe staff levels, as well as the roll-out of last year's strike settlement, were also among the issues discussed at the meeting.
INMO General Secretary Phil Ní Sheaghdha said that over 32% of all confirmed Covid-19 cases in Ireland are healthcare workers and that nurses and midwives make up a large number of that proportion.
Speaking on RTÉ's News at One, she said the figures are "much higher than in other countries and that causes us great concern."
She questioned if some HSE policies had contributed to the figures, citing fatigue of healthcare workers as one factor suggested that could have negatively influenced the numbers.
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She said that more information is needed so the figures can be scrutinised.
Ms Ní Sheaghdha said "we need to look at where infections are happening" and to see where relief needs to be given in order to ensure that fatigue does not set in.
She said because of staffing and workplace issues in some cases derogations given to staff who are positive with Covid-19 may not have been fully implemented and this needed to be looked at.
In relation to the wearing of personal protection equipment, she said that the INMO is not confident that its members are getting proper instruction about where it is needed.
Ms Ní Sheaghdha said that Mr Harris also agreed to set up a meeting this week with the Department of Children to consider what childcare proposals are now being looked at to assist healthcare workers.
SIPTU also described today's meeting with the minister as highly productive.
Health Divisional Organiser Paul Bell said the union was satisfied that Mr Harris fully understood its concerns and that all of its questions would be answered in due course.
Overall the latest figures on Covid-19 show a stabilising trend regarding the impact of infection in Ireland, but the number of new cases has increased slightly in recent days.
The number of additional cases reported yesterday was 77 and means new cases have remained under 100 per day since 22 May.
There have been 25,062 confirmed cases of the coronavirus here.
One further death was reported yesterday bringing to 1,650 the number of patients who have died from Covid-19.
Of those people who have died from the virus, 90% had an underlying health condition.
Figures published today show there are 330 patients in hospitals with confirmed or suspected Covid-19.
There are 37 patients in intensive care beds with the virus, plus 20 suspected of having Covid-19.
The latest HSE Operational Report up to last night shows that there are 120 ICU beds vacant and across the acute hospital system, there are 948 vacant beds.
The National Public Health Emergency Team will meet on Thursday to review the overall figures and will give a recommendation to Government on whether Ireland should move to Phase 2 of easing restrictions next Monday.
Any negative impact of the lifting of restrictions under Phase 1 will be seen in the figures this week.
Overall the latest figures on Covid-19 show a stabilising trend regarding the impact of infection in Ireland, but the number of new cases has increased slightly in recent days.
The number of additional cases reported yesterday was 77 and means new cases have remained under 100 per day since 22 May.
There have been 25,062 confirmed cases of the coronavirus here.
One further death was reported yesterday bringing to 1,650 the number of patients who have died from Covid-19.
Of those people who have died from the virus, 90% had an underlying health condition.
Around 80% of cases of Covid-19 will be a mild to moderate illness, close to 14% have severe disease and around 6% are critical.
Generally, you need to be 15 minutes or more in the vicinity of an infected person and within two metres of them, to be considered at-risk, or a close contact. Meanwhile,
