The Minister for Health, Micheál Martin, says there has been a very positive response to the smoking ban.
During the first day of the ban he said there had been strong support from the general population.
Legislation banning smoking in enclosed workplaces came into effect at midnight last night.
The new regulations mean that it is illegal to smoke in certain confined working environments. However, there are some exemptions such as prisons and the bedrooms of hotels.
The bar workers' union, Mandate, has said early feedback from its members showed that the smoking ban will work, and that it has the support of the general public.
The union was responding to the claims by the Vintners' Federation of Ireland that the ban is unenforceable, and that business is already down in pubs as a result of the ban.
When Mr Martin announced the smoking ban, he said he had no option. Experts had told him that 150 bar workers a year would get lung cancer from passive smoking in pubs if the ban was not introduced.
Speaking on RTÉ Radio earlier today, Mr Martin said that the ban has opened up an important debate on public health. He added that it is part of a wider strategy to improve the country's cardiovascular health.
Mandate predicts significant benefits
There has been significant trade union support for the measure, as well as from the medical world.
Mandate's John Douglas said today that there will be significant health benefits from the measure. He said many of his members spend over 14 hours a day in pubs, and are experiencing immediate benefits.
Mr Douglas said the public was not being antagonistic towards bar workers. He predicted the ban will work on the basis of public pressure.
VFI warns of repercussions
Tadhg O'Sullivan of the Vintners' Federation of Ireland warned there would be political repercussions for Government parties from those who oppose the ban.
He said jobs would be lost and that already business was down in many pubs.
The introduction of the ban has been welcomed by a number of lobby groups. A survey carried out for the Office of Tobacco Control indicates that most people are likely to comply with the ban and notes strong public support for the measure.
The Irish Hotels Federation has encouraged anyone using their members' facilities to show patience and tolerance while the new legislation is implemented.
Call for similar ban in the North
Anti-smoking campaigners in the North have responded to the introduction of the ban by lobbying for similar legislation from the British government.
A spokeswoman for the Institute of Public Health, Dr Jane Wilde, said the Stormont Minister for Health was aware of how many lives would be saved if workers were protected by a similar ban.