The Health Service Executive (HSE) says it expects the coronavirus to start spreading within communities in the next few weeks.
The six cases confirmed in Ireland so far have been linked to travel from northern Italy, one of the affected areas.
Four members of the same family in the west were the latest to test positive, leading to a number of schools in Co Clare being closed.
Efforts are underway to trace anyone the four people may have been in contact with.
Dr Sarah Doyle from the HSE says everyone needs to take action to limit the spread.
"We expect that this novel coronavirus will be spreading within our community within weeks.
"The onus is on all of us to protect those who are invulnerable groups and to protect our healthcare workers".
"So everybody needs to get ready: we need to think about how the virus is spread and think about how you can prevent it spreading".
It comes as Cork University Hospital has cancelled all outpatient appointments for Friday.
It says this is due to "infection control issues".
It adds that all patients will be re-scheduled as soon as possible.
There have also been three confirmed cases in Northern Ireland.
While Britain has recorded its first coronavirus-related death.
The patient, who had with underlying health conditions, was admitted to hospital on Wednesday evening and tested positive for the virus.
Meanwhile the HSE chief, Paul Reid, says an extra €20m is being 'immediately invested' to open 25 more intensive care beds in Irish hospitals to prepare for any surge in coronavirus cases.
He spoke to The Pat Kenny Show earlier in the wake of the latest confirmed cases here.
Mr Reid noted that Ireland is still in the containment phase and therefore working to limit the number of cases here.
He explained: "We're looking in the first instance to avoid a surge into our hospitals and acute settings - but we acknowledge that at some point that that's a possibility we have to prepare for."
Health officials decided earlier this week to put in place more ICU resources across the country as part of their preparations for any increase in cases.
Mr Reid said: "We've immediately put in place a €20 million investment to bring on another 25 ICU beds... that's a very significant investment, way above anything we've done in the last long number of years.
"The money and the funds are there to staff [the new beds]. We will be commencing the process to recruit and deploy staff into those areas."
He also said decisions will be made on what to prioritise in hospitals if there is a surge in cases, saying it will be about 'maximising the capacity' of the resources already in hospitals.
'Clear message to the public'
According to Mr Reid, data so far has shown the vast majority of people (around 80%) infected with the coronavirus will not be seriously ill - and many won't have any significant symptoms.
However, he also said it's important to prepare hospitals to treat those who do become seriously ill - noting that data from around the world suggests that around 5% of people become critically ill.
Current figures show also there has been around 3,300 deaths out of around 96,000 confirmed cases.
Mr Reid reiterated that people should follow official advice when it comes to things such as hand-washing or travel to areas impacted by the outbreak.
He said: "We don't and shouldn't create a sense of panic, and neither do we want a sense of complacency.
"My very clear message to the public today is we do need you to act: we need you to take it responsibly, we need you to take our advice seriously, and if you do we will contain this for as long as we possibly can."
He also thanked all of the public health workers involved with the response to the coronavirus cases here - saying it is "very inspiring" to see how they've responded.
Additional reporting: Jack Quann