The HSE chief is encouraging everyone over the age of 18 to register for their vaccine to help "turn the tide" on the Delta variant.
It comes as the Department of Health confirmed a further 1,345 cases of Covid-19.
The number of Covid patients in hospital down one to 105 while there is also one less patient with the virus in ICU bringing the number to 21.
Covid patient numbers in hospital have risen from 50 to 105 which is the highest level in almost two months.
The highest number of Covid-19 cases in nearly six months was also confirmed yesterday with 1,386 new infections.
Dr Eoghan de Barra, a consultant in infectious diseases in Beaumont Hospital, says hospitalisations will continue to rise.
"We know from before once it starts to happen it's likely the rate of increase will accelerate," he said.
"Hopefully, the majority of people will have very mild disease and not be anything like the severity that we have seen in previous waves."
Dr de Barra said he would not be surprised to see hospital numbers double in seven days.
"It's hard to know exactly what the impact of vaccine and the impact of lifting restrictions will be because now we are lifting restrictions and increasing mixing in the setting of increasing cases. We haven't done this before."
Dr de Barra said the main message that he wants to get out to people is to get a vaccine at the earliest opportunity.
Over 50,000 vaccine doses were administered yesterday, according to the HSE chief.
Paul Reid encouraged everyone over the age of 18 to register, saying: "If you are fully vaccinated, you have high levels of protection against being hospitalised or ICU."
The Junior Children's Minister has called for Covid-19 vaccine registration to open for teenagers straight away.
It is after the European Medicines Agency (EMA) authorised the Moderna jab for 12 to 17-year-olds yesterday.
The EMA had already approved the Pfizer jab for this cohort but the National Immunisation Advisory Committee (Niac) has yet to give guidance for its rollout here.
Minister of State, Anne Rabbitte, says children should be vaccinated as soon as possible.
She said there are many vulnerable children around the country who need the vaccine.
"I would strongly recommend that children who are medically compromised are prioritised and done as soon as possible," said Ms Rabbitte.
"I think waiting until September for those children is too long."