The Department of Health has been notified of 320 new cases and no further deaths due to Covid-19.
In a statement, the National Public Health Emergency Team said there has been 4,718 coronavirus-related deaths in Ireland and a total of 238,466 confirmed cases.
As of Friday 2 April, 923,878 vaccine doses were administered in Ireland.
NPHET said that 655,292 people have received their first jab, while 268,586 people have been given a second dose.
The Health Service Executive said that it will have administered one million vaccine doses this week.
The vaccination of people aged 70 and older is continuing and more than 42,000 people at very high risk have been given a jab.
Towards the end of April, the campaign will move to vaccinating people aged 65 to 69.
Latest figures show that 260 people with Covid-19 are being treated in hospitals, down 87% from the peak on 18 January when 2,020 people with the disease were hospitalised.
There are 58 patients with the disease in intensive care units, a 73% reduction since 24 January, when 221 cases were in ICUs.
Minister for Health Stephen Donnelly said on Twitter that "real progress is being made."
Some good news on Easter Monday. Over 30,500 vaccines were administered on Friday 👏👏 We'll reach the 1 Million vaccinations milestone this week. Real progress is being made. https://t.co/4pihen6Esf— Stephen Donnelly (@DonnellyStephen) April 5, 2021
Tánaiste Leo Varadkar said the vaccination programme will be "accelerated in coming weeks".
In a post on Facebook, he said that "a lot of people might feel like they are never going to be vaccinated but we are going to surprise you.
"We are going to see the vaccine programme being accelerated in coming weeks. By the middle to the end of May we anticipate that the majority of adults will have had their first dose and the over 70s will be fully vaccinated.
"By the end of June the vast majority, more than 80%, of adults will have had their first dose and we hope we can do even better than that."
Mr Varadkar said the change to an age-based system made sense due to the higher mortality rates among older people.
He added that for businesses worst impacted by the pandemic, it was "well accepted and recognised" that financial supports would have to continue beyond 30 June.
There were two further deaths linked to Covid-19 in Northern Ireland in the past two days and an additional 89 positive cases, the Department of Health said.
'Late evening' as GP to administer vaccines after delivery delay
A Kildare-based GP said he was forced to cancel vaccination plans for over 50 patients this afternoon because the vaccines did not arrive.
Dr Adrian McGoldrick said that staff had been at the clinic since early morning preparing and the jabs were due to be delivered between 12pm and 1pm, but there was no delivery and no contact number available.
However, he said the vaccines arrived this evening and patients who had been sent home were called back in to receive them.
Earlier, in a social media post Dr McGoldrick described the situation as "utterly frustrating for all."
"I have just looked into my waiting room to see a 93-year-old man who is bedridden but his son physically carried him in for the vaccine and now he has to be rescheduled."