Taoiseach Micheál Martin has urged the public to shop safe as the country eases out of the second lockdown.
Some non-essential retail and other businesses reopened on Tuesday after six weeks of Level 5 restrictions.
The lifting of restrictions also saw the hair and beauty industry and gyms and leisure centres open their doors after six weeks of closures.
Restaurants and pubs that serve food will remain shut until Friday in line with the Government’s plans to reopen on a phased basis.
There were some queues outside stores early on Tuesday but trade otherwise appeared steady as people returned to the shops ahead of Christmas.
Mr Martin issued a message to the public as he paid a visit to the Kilkenny store in Dublin on Tuesday.
“Take a little time to investigate off-peak opening times, ensure you wear a mask on busy streets as well as inside shops and shopping centres,” he said.
“Think about what you need to buy in advance so that you do not spend too much time in the shops browsing. Plan to shop as early in the month as possible and please respect priority plans in stores for vulnerable people who may need a little extra help when shopping.
“When planning your Christmas shopping, please support your local retailers and businesses. It has been a difficult year for small local businesses, so please consider your local businesses when deciding on your gifts this year.”
As Covid-19 restrictions eased country-wide, health chiefs issued warnings not to gather in crowded areas.
This morning, the number of #COVID19 cases in hospital has come down again to 222 with 30 in ICU. Today, as society & the economy opens up, let's all take precautions to value & protect into December the great progress that we've made. We all want to open up & stay safe.@HSELive
Advertisement— Paul Reid (@paulreiddublin) December 1, 2020
Chief medical officer Dr Tony Holohan also said that office Christmas parties should not be happening and pointed out the link between infection and socialisation while urging people to reduce their number of contacts.
He said alcohol has been “a very significant common factor in a lot of the kinds of social experiences in which transmission has occurred”.
Eighteen further Covid-19 linked deaths were reported in the Republic on Tuesday, along with an additional 269 confirmed cases of the virus.
HSE boss Paul Reid tweeted on Tuesday: “Today, as society and the economy opens up, let’s all take precautions to value and protect into December the great progress that we’ve made.
“We all want to open up and stay safe.”
Gardaí plan to scale back many of their checkpoints as the country moved from Level 5 to Level 3.
The fixed checkpoints on motorway and dual carriageway routes will no longer be in place.
However, under Operation Fanacht more than 100 checkpoints will remain in place on main routes to monitor inter-county travel.
Gardaí said there will also be patrols that will focus on the night-time economy.
As restrictions eased, wedding guests and mourners at funerals will be limited to 25 while no organised indoors events are permitted.
Gatherings of up to 15 people are allowed outdoors, while non-contact training may take place outdoors and in pods of 15, and individual training is permitted indoors.
Gyms, leisure centres and swimming pools reopened for individual training from Tuesday.
Hotels, B&Bs and non-essential retail also resumed trading.
People are still being urged to work from home and public transport is limited to 50 per cent. People have also been advised to stay within their own county.
Places of worship, museums, galleries, libraries and cinemas will also reopen, but wet pubs are closed except for takeaways.
The Government has also recommended that the public should wear face coverings in crowded places.
