The Department of Health has said two patients who contracted human swine flu (H1N1) are being treated in intensive care units.
Speaking at a swine flu update this afternoon, the chief medical officer at the Department of Health Dr Tony Holohan said the HSE expects some deaths from the virus, and further hospitalisations, over the coming weeks and months.
Dr Holohan said 12 people have been hospitalised so far.
A man in his 30s, who was admitted to St James's Hospital last week remains 'critically ill' with the virus.
It is believed the man, who is originally from Bratislava in Slovakia, contracted the virus abroad. He has been working in Ireland for several years.
The hospital said that all necessary precautions were being taken and that the Health Service Executive and the Department of Health were being fully informed.
The Department of Health said the anti-viral Tamiflu will in future only be given to people with severe symptoms, or those at high risk of the illness.
It will not be prescribed to treat people with mild symptoms or to prevent people getting the virus.
The Department of Health says 278 cases of laboratory confirmed human swine flu have been reported in Ireland.
There have been 32 cases of person-to-person transmission.
Dr Darina O' Flanagan of the Health Protection Surveillance Centre said that around 500 people a week are now attending their GP with cases that are most likely human swine flu.
Dr Pat Doorley, HSE National Director of Population Health, said that the delivery of 7.7m doses of a vaccine could take place over 6 to 12 months.
The Department will no longer be giving daily figures on cases, instead it will rely on weekly reports from 50 GPs as part of a national influenza monitoring network.
The current trend is around 13.1 cases for every 100,000 of the population - representing around 500 cases week.
Meanwhile, a Down v Dublin Minor Championship game scheduled to take place 31 July has been postponed due to swine flu fears.
A 'serious viral infection' within the Down minor panel has affected the overwhelming majority of the Down players, according to a statement from the GAA.
816 deaths worldwide
The World Health Organisation says there have been 134,503 confirmed cases of human swine flu and 816 deaths from the virus.
However as countries are no longer required to test and report individual cases, it says this is an underestimate of the real number of cases.
Meanwhile, in the UK the BBC may be asked to clear its schedules for educational programmes if schools are closed due to swine flu.
Ministers are understood to have had discussions with the Corporation as part of its contingency planning for the pandemic.