It is likely that flu activity peaked before Christmas, the HSE has said, but figures remain high with 2,049 cases recorded in the week to last Saturday.
It compares with 1,777 cases the previous week, while the week before Christmas saw the highest number of cases at 3,547.
HSE Chief Clinical Officer Dr Colm Henry said 632 patients are sick with respiratory illnesses across the hospital system.
He said considerably more are presenting to GPs and out-of-hours services and that the impact of respiratory illnesses has been significant, including on emergency departments.
Dr Henry said that the HSE modelling had predicted a peak around Christmas and that had happened, but it did not translate into as much hospital admissions as had been feared.
Dr Henry said a lot of this was down to the vaccine uptake and the way GPs and hospitals operated to deal with the situation.
He said that the system is still seeing considerable pressure and he expected to see ongoing transmission of influenza in the weeks ahead.
Dr Henry said that health staff had worked hard to deal with the pressures, including GPs putting on extra clinics.
The Health Service Executive has also urged caution with the latest figures, as the data is affected by the Christmas and New Year holiday period and reporting, testing and other changes in the health system at this time.
In terms of the impact on the health system, the HSE said there were 700 people in hospital with flu, or the respiratory syncytial virus (RSV) at the start of this week.
In the week to last Saturday, figures show there were 588 RSV cases, 216 Covid-19 cases and 35 norovirus cases.
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The HSE said that every winter brings an increase in seasonal illness such as flu.
It added that while these illnesses are unpleasant but mild for many, they can be very serious for older adults, young children and people with underlying health conditions.
The HSE said that getting vaccinated remains the best protection against serious illness and hospitalisation.
Nursing Homes Ireland has said that outbreaks are still being seen in nursing homes but are being managed.
It added that vigilance remains high across nursing homes, particularly given increased visitor activity over the recent holiday period.
Meanwhile, there are 670 admitted patients waiting for a hospital bed, according to the Irish Nurses and Midwives Organisation.
The hospital worst affected is University Hospital Galway with 81 patients waiting, while there are 78 patients waiting at University Hospital Limerick and 73 at Cork University Hospital.
The HSE figures put the trolley numbers lower at 428.
