Hairdressers and barbers will reopen on June 29, and gatherings of up to 50 people indoors allowed after the government brought forward a series of relaxation measures.
Taoiseach Leo Varadkar said that after studying advice from the National Public Health and Emergency Team (NPHET), Cabinet approved the rephasing of the road map.
Mr Varadkar said that, apart from some exceptions, most things are now being moved to phase three beginning on June 29.
These include the reopening of churches and places of worship, gyms, cinemas, leisure facilities, hairdressers, beauticians and barbershops.
Mr Varadkar also said that all sporting activities, including close contact sports, can recommence.
While people are still advised to work from home if they can, mass gatherings of people will be limited to 50 people indoors and 200 people outdoors in phase three.
This will rise to 100 people indoors and 500 people outdoors on July 20.
Speaking at Government Buildings in Dublin, Mr Varadkar said: "As a country, we got through this without giving way to despair by looking out for each other and by staying hopeful.
"The spirit of hope proved to be contagious has brought us to where we are now, ahead of schedule, able to accelerate the opening of our society and our economy.
"I'm making this announcement today to give people time to prepare so the places can be ready to reopen.
"But we all need to stay careful. It will not be as it was before the start of the pandemic.
"For now sports will take place with very limited numbers of spectators.
"We are making progress but this announcement comes with terms and conditions. The virus hasn't gone away, we're all still susceptible.
"As our country is reopened in a controlled and measured way, personal responsibility will become more important than ever before.
"So we're asking people to consider four things before making a decision about doing something and at all times evaluate the risk for yourself and to others.
"These four things are - distance, activity, time, and environment or Date for short.
"Distance - always try to stay two meters apart from somebody else if possible.
"Activity - wash your hands regularly, wear a face covering on public transport or in a crowded indoor place like a supermarket.
"T for time. The length of time and the amount of time you spend with a person or group increases your risk, and the environment, always bear in mind that a closed poorly ventilated indoor space is much riskier than being outdoors.
"Taking responsibility means not entering your place if you see that is packed. It means leaving somewhere, even if you're having a good time, if you've been there for too long.
"It means exercising judgment and self control."
Mr Varadkar said there is more work to do and said the next road map will be for economic recovery.
He said the public need to show the same "determination and ambition" in leading economic recovery and creating new jobs.
"Many people have asked how quickly can we bounce back, and how long will it take before our economy returns to where it was before," he added.
"The truth is we cannot know for sure. Some have asked whether there's a limit to what we can achieve. My answer is that limit does not exist.
"We've been here before and we know the way we know what needs to be done and the next road map will be a road map for economic recovery, the National recovery plan."
Today, Ireland's coronavirus death toll rose to 1,714 after a further two deaths were announced by the NPHET.
There were 13 new confirmed cases of the virus in Ireland, taking the total to 25,368 since the Covid-19 outbreak began.