People aged 70 and over should have received both doses of their Covid-19 vaccine by mid-May, the Health Minister has said.
Stephen Donnelly said that despite disruptions to the supply chain, and changing delivery schedules, it should still be possible to vaccinate the entire population by September as planned.
But he warned that this projection is based on "highly conditional forecasts".
Vaccination of the over-85s group will begin from Monday, with over 20,000 doses of the Pfizer and Moderna vaccines to be distributed to GPs next week.
That figure will rise to 50,000 the following week, Mr Donnelly told the Dáil.
He said: "The schedule I have would suggest that the group (over 70s) will have finished their second doses by mid-May.
The timeline was criticised by Sinn Fein health spokesman David Cullinane.
He said: "I accept that there are supply issues, but the middle of May, for all of the over 70s to be inoculated, it's a long time for those most at risk to be waiting.
"And I think that will cause concern for many older people."
As of Sunday, 272,000 vaccines have been administered in Ireland, Mr Donnelly said.
Vaccination of the over 85s cohort is to begin on Monday through GPs' surgeries.
Alternative arrangements will be made for those unable to travel to their GP, the Minister said.
He said: "There will be people who can't make the journey to a GP and local solutions are being put in place for them."
He said: "Next week, the plan is to distribute approximately 20,000 mNRA vaccines to the GP network, specifically for the 85 and older group.
"That's about 10,000 doses of Moderna and 12,000 doses of Pfizer.
"The following week, we're planning to increase that to around 50,000 vaccine doses.
"The plan is to increase that again the week after that.
"As with all vaccine forecasts, these plans are entirely dependent on supplies arriving in to Ireland."
Mr Donnelly said that 5,800 vaccinators have been trained to date, but that many more will be needed.
The latest information shows that 85% of people say they will definitely or probably take the vaccine.
Some 3,000 residents and staff in nursing home settings have yet to receive the vaccine, the Dáil heard.
This has been complicated by Covid-19 outbreaks, with people unable to receive a vaccine for 28 days after contracting the virus.
The Minister also defended the EU over its handling of the vaccine rollout, which has come in for heavy criticism.
He said: "The EU27 approach is the right one for Ireland, and for Europe as a whole.
HSE chief Paul Reid described next week as an exciting new phase of the vaccination programme.
He said Ireland is currently third in Europe in terms of doses per 100,000 of the population, behind Malta and Denmark, and "well above the EU average".
Speaking at the HSE weekly briefing, he set out plans for the first 12,000 people from the over 85 age group to be vaccinated in 84 GP practices across 20 counties.
Mr Reid said where some may not have transport to get to vaccination locations, the HSE will work with local authorities, Civil Defence, and the Defence Forces.
Meanwhile Dr Colm Henry has said there have been 740 reports of side effects of the vaccine, most commonly a sore arm, mild fever and mild flu-like illness.
Work is also continuing on mass vaccination centres.