Thousands of people are facing disruption, as members of the Irish Nurses and Midwives Organisation (INMO) are staging another day of strike action.
Some 37,000 nurses and midwives have taken to the picket line over pay and working conditions.
The number of services on strike has also increased from 82 to 240.
Up to 50,000 people will be affected by the action - with all outpatient appointments, surgeries and routine community nursing activities cancelled.
Local injury units and nurse-led day centres for older people and those with disabilities are also closed.
The advice is to stay away from emergency departments.
The HSE's mental health services are facing disruption too, as the Psychiatric Nurses Association (PNA) are extending an overtime ban on Wednesday and Thursday, in their own row over pay and working conditions.
The dispute is centred on pay issues and working conditions within Irish hospitals, which unions have warned are causing the recruitment and retention crisis in the health service.
Nurses are demanding pay increases of about 12% - and for the Health Service Executive (HSE) to take steps to deal with recruitment and retention issues.
The Government has insisted it will not do a special deal for health workers, and said any pay increase would open the floodgates for other public service unions to seek the same.
A Government offer of talks has been rejected, as the proposed discussions would focus on "issues other than pay".
Joint statement from Minister for Health @SimonHarrisTD & Minister for Finance, Public Expenditure & Reform @Paschald on the current nursing dispute. pic.twitter.com/2LXr2wcInL
— Department of Health (@roinnslainte) February 4, 2019
Reacting to the statement, INMO General-Secretary Phil Ní Sheaghdha said: "This is spin masquerading as substance. Government by press release is unfair and confusing to patients and insulting to nurses and midwives on the picket lines.
"Recycling broken promises is no way to build good-faith negotiations.
"The Government's press release refers to non-pay issues which are already agreed since 2017.
"The INMO previously referred the Government to the Workplace Relations Commission (WRC) to try and find a solution to this dispute, but the Government failed to engage or make any proposals.
"Talks at the Labour Court sadly produced similar results.
"We have identified excessive costs and wastage in the HSE, which could be used to address the pay issues at the heart of the recruitment and retention crisis. But the government simply will not listen."
