The INMO has announced two additional dates for the nurses and midwives strike, with an increase in the number of services on strike rising to 240.
Strikes days will take place on 19 and 21 February, in addition to dates set for 5 and 7 February, and from 12-14 February.
The INMO has also said it will be organising a national rally on Saturday 9 February.
In a statement, INMO General Secretary Phil Ní Sheaghdha said: "Everybody – except the Government – recognise that there is a serious understaffing problem in our health services. The public support for the strike on Wednesday showed that the Irish people stand with nurses and midwives."
She added: "Our message is clear. We will not be going away – resolving this dispute requires direct engagement from the Government, recognising the real recruitment and retention problems in Irish nursing and midwifery.
"We simply want to be able to do our jobs, but our health service cannot hire enough nurses and midwives on these uncompetitive wages.
"As ever, we remain available for talks with the government for any realistic proposals."
In response, the HSE has said it remains available to engage in any efforts to avert industrial action.
"We are continuing to engage with the INMO to put in place arrangements for the safe provision of services in advance of next Tuesday's strike," it said.
A spokeswoman for the Minister for Health said that Simon Harris regrets the decision taken by the union.
She said the minister believes there is an onus on both sides to engage in discussions to avoid the dispute.
In addition to the nurses' action, mental health services have experienced disruption around the country as the Psychiatric Nurses Association implemented its overtime ban.
The PNA Officer Board will meet on Monday to review the situation.
The PNA's 6,000 nurse members will have further overtime bans from 5-7 February.
The association plans to escalate this to a three-day strike from 12-14 February when the 37,000 members of the INMO are also due to be on strike
