Members of the public who refuse to wear a face mask on public transport from Monday face fines of €2,500 or six months in prison when the measure becomes mandatory.
Gardai can also be called, but confusion surrounds who will police the measure.
Would-be passengers who are not wearing a mask may not be allowed on board public transport, Taoiseach Micheal Martin warned yesterday.
However, the union for bus and rail drivers said its members will not be enforcing the rule.
The National Bus and Railworkers Union said potential confrontations and conflict between staff and passengers could risk compromising the safe operation of services.
Mr Martin said there would be provision for gardai to be called in exceptional circumstances, but he envisaged good compliance from the public.
"The wearing of masks on public transport will be compulsory from Monday," he said.
He was speaking as 25 more people were diagnosed with Covid-19, one of the highest daily tolls since mid-June.
It confirms the upward trend in new cases, which is partly due to a rise in travel-related infections and the spread of disease among young people who are socialising and not physically-distancing.
Another death from the virus was also announced yesterday, bringing the total number so far to 1,744.
Gardai are expected to crack down on street revelry and breaches of safety measures in pubs this weekend in a bid to avoid last week's scenes of abuse of physical-distancing in Dublin city centre.
Mr Martin warned young people that "no one is invincible" from Covid-19 as he urged them to behave responsibly.
Crowded indoor gatherings and house parties are "a problem", he said, adding: "The gardai will be out this weekend to prevent a recurrence of what happened last weekend."
His appeal was echoed by Health Minister Stephen Donnelly and Acting Chief Medical Officer Dr Ronan Glynn.
Dr Glynn said: "This weekend, we all have an opportunity to exercise, socialise and enjoy life in a safe and responsible way."
Meanwhile, the HSE has warned the public about a telephone and text scam from criminals abusing the new Covid-19 tracing app, which has been downloaded by 1.1 million people.
The fraudsters are claiming to be HSE contact tracing and testing staff. The calls and text messages claim the person has been identified as a close contact of someone who has Covid-19.
They ask for money for a testing kit to be sent to them and for bank details.
A statement from the HSE said: "The HSE does not charge the public for Covid-19-related services, including testing, and such texts and calls should be ignored.
"Any close contacts of a confirmed positive case of Covid- 19 will be contacted by the contact-tracing team or public health staff and referred for a test.
"The HSE does not charge or ask for payment for testing.
"If the Covid-19 Tracker App has identified you as a close contact, you will see a red box with the advice on what you should do next on all pages of the app. You will never be asked to pay for testing
"If you are concerned or suspicious, please ring HSE Live on 1850 24 1850 and contact your local gardai."