About 1.9% of Ireland's population has been given the Covid-19 vaccine, according to the health minister.
Stephen Donnelly said that, by Sunday night, 94,000 vaccines were administered, with 71,000 frontline healthcare workers and 23,000 of residents and staff of long-term care facilities inoculated.
The country's vaccination programme is focusing on three priority groups over the next couple of months, including long-term care residents, frontline healthcare workers and those aged over 70.
The Government has committed to having these groups vaccinated by the end of March, which would see 1.4 million doses administered.
In a tweet, Mr Donnelly said that those who were among the first to receive the first dose of the vaccine, will now be receiving the second.
This includes 79-year-old grandmother Annie Lynch, from Dublin, who became the first person in the Republic to receive the jab on December 29.
Mr Donnelly tweeted: "I've received an update on our vaccination programme and by Sunday night we had given 94,000 vaccines, 71,000 to our frontline healthcare workers and 23,000 to residents and staff of long-term care facilities.
"Well done to all involved including @AmbulanceNASand @defenceforces.
"This week we are also seeing the first of our dose two vaccinations happening - so Annie Lynch and those who were among the first in the programme will be getting the second vaccine.
"We have now vaccinated about 1.9% of our population.
"Our vaccination journey is just beginning and there'll be bumps on the road but great credit to (Paul Reid) and his team for this achievement while also caring for large numbers of patients with Covid in our hospitals."
The number of people with the virus being treated in hospital dropped to 1,954 on Tuesday morning - the first time the daily figure has decreased in a number of weeks.
The number of people with Covid-19 in intensive care units remained at 199.
The 14-day incidence of the virus stands at 1,404 cases per 100,000 population.
Mr Donnelly is to ask the Cabinet today to sign off on an agreement with GPs and pharmacists to administer the vaccines.
The proposed deal would see GPs and pharmacists paid 60 euro for each patient vaccinated.
Meanwhile, the president of Sinn Féin Mary Lou McDonald said the controversies at Coombe Hospital and Rotunda Hospital, in which family members of staff received the vaccine, has raised questions marks.
It emerged in recent days that two family members of staff at the Rotunda Hospital and 16 family members of staff at the maternity hospital received the coronavirus vaccine.
Spokespeople for the hospitals said the vaccines would have been wasted otherwise.
Ms McDonald told RTÉ's Today With Claire Byrne show.
"But the idea that there are spare vaccines that could be dispensed in accordance with just the judgment of an individual, and that in some cases those vaccines would go to family members, it isn't acceptable.
"In fairness, the master of the Coombe has acknowledged and has apologised. This can't happen again.
"The wider concern is the necessity for very, very clear guidance in a timely fashion so that all those who are charged with dispensing these vaccines, safely and in an order of priority, are very clear what the instruction is.
"It raises just a question mark as to why that wasn't clear and why that wasn't there from the get go.
"We're not dealing with the vast, vast quantities as of yet of vaccines.
"We're dealing with a very limited supply, so it is astonishing, therefore, that the clearest of guidance wasn't available to everybody, given that this is such a scarce and such a precious resource at this point."
The HSE said standby lists of healthcare workers available at short notice are in place to ensure doses of Covid-19 vaccines that are about to expire are used.
The protocol was put in place on January 12 after excess doses were given to family of staff members at the Coombe and the Rotunda.