The HSE has described the rise in respiratory illnesses as "substantial" and said that pressure is increasing on the hospital system.
It reported a further increase in cases of influenza, Covid-19 and Respiratory Syncytial Virus (RSV) in the week to last Saturday, when it was notified of 1,628 cases of influenza - almost double the number compared to the previous week.
Some 414 patients were hospitalised due to flu.
Covid-19 cases doubled to 1,200 cases in the week to last Saturday and 459 patients were hospitalised.
Cases of RSV increased to a lesser degree by 121 cases to 465 and 147 patients were hospitalised.
The HSE added that RSV activity peaked in early December and the recent slight rise is due to socialisation over the festive period and the return to school and childcare.
It said that the Covid-19 numbers are the highest since the wave in August last year.
Health officials believe that cases of infectious diseases will peak in the next week or two.
So far this winter season, there have been 8,652 cases of Covid-19, a total of 6,747 cases of RSV and 4,931 cases of influenza.
Dr Gerry McCarthy, Clinical Lead for HSE National Programme for Emergency Medicine urged people to treat their symptoms at home rather than attending a hospital if possible.
He also said that anyone going to a hospital with respiratory symptoms should wear a mask.
Figures from the Irish Nurses and Midwives Organisation put the number of patients waiting for admission to a bed on Wednesday at 605.
The HSE calculate the figures differently, and put the number lower at 409.
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Speaking on RTÉ's Morning Ireland, Dr McCarthy said that the country is seeing a "steady increase in Covid, certainly a 77% week-on-week (increase)".
"There has also been a 92% increase in flu, but RSV is more stable than that," he added.
"We're seeing the usual rise in infectious diseases a little bit later this year than last year so we're expecting it to peak in the next week or two."
Dr McCarthy urged people to treat their symptoms at home rather than attending a hospital where possible, but said anyone with respiratory symptoms who do attend an emergency department should wear a mask.
He said: "If a person comes to hospital with any suggestion of respiratory illness and they’re not already wearing a mask, they certainly (will) be provided with one and all staff dealing with them will be masked up.
"Many hospitals are deciding on their own bat, based on their local data of what kinds of patients and how many inffective illnesses are coming in, to have mandatory mask wearing.
"I think we should be increasing the wearing of masks at the moment."
The HSE has said that the cold weather has seen a significant increase in emergency department attendances for slips, trips and falls.
Dr McCarthy, who is a consultant in emergency medicine at Cork University Hospital, urged people to take precautions during the cold snap.
He said: "Walk on the sunny side of the street because that tends to be less icy.
"Ask yourself, do you really need to go for that run before work this morning or can it wait till later? And will the paper still be in the shop if I wait a couple of hours before going to get it.
"And most importantly, stop looking at your phone as you're walking along."
WHO warns Covid still a threat
Meanwhile, almost 10,000 Covid-19 deaths were reported in December, the WHO said earlier, as it warned the virus remained a major threat despite partially passing under the radar.
The World Health Organization said data from various sources pointed to increased transmission last month, fuelled by gatherings over the Christmas holiday period and by the JN.1 variant, which is now the most commonly-reported around the globe.
"Although Covid-19 is no longer a global health emergency, the virus is still circulating, changing, and killing," the UN health agency's chief Tedros Adhanom Ghebreyesus said.
Besides the near 10,000 deaths reported to the WHO last month, there was a 42% increase in hospitalisations and a 62% increase in intensive care unit admissions, compared with November.
However, the figures are based on data from less than 50 countries -- mostly in Europe and the Americas, he said.
