More than 200 pubs, restaurants and hotels were found to be in breach of the smoking ban in its first month of operation.
However, out of a total of over 7,500 premises inspected by health authorities during this time, 97 per cent were found to be in compliance with the law.
Market research commissioned by the Office of Tobacco Control (OTC) also suggests that visiting patterns to pubs and restaurants have remained constant.
While the number of non-smokers visiting pubs has increased slightly since the introduction of the new law, the number of smokers visiting has remained the same, according to research by TNS mrbi on public attitudes and behaviours.
It also found that almost one in five smokers chose not to smoke at all when out socialising.
The Minister for Health, Mr Martin, yesterday welcomed publication of the figures and said they reflected the "widespread public support and goodwill that exists for a healthy smoke-free environment in the workplace".
Results from a month of inspections by health authorities show compliance rates of well over 90 per cent in all parts of the State.
Compliance rates were lowest in the Western Health Board (92 per cent) and the North-Eastern Health Board (94 per cent). The highest compliance rate was recorded in the Mid-Western Health Board (99 per cent).
There have been no prosecutions arising from flouting the smoking ban yet, although officials say a number of cases are pending.
An overall compliance rate of 87 per cent was recorded in relation to the erection of no-smoking signs. The lowest rate (77 per cent) was in the North-Western Health Board area and the highest (99 per cent) in the Southern Health Board.
Regarding the smoke-free compliance phone line (1890 333100) in operation by the OTC since March, almost half of all calls were complaints, while prank calls accounted for a quarter.
The OTC's chief inspector, Mr Dave Molloy, said much of the compliance effort was directed specifically at the hospitality sector in response to concerns expressed by the licensed trade over implementation of the ban.
"This is reflected in the statistics. Sixty-six per cent of the inspections related to licensed premises, with compliance levels of 96 per cent for the smoking prohibition and 89 per cent in respect of the requirement for 'No Smoking' signage," he said.
Research also demonstrated that the benefits of smoke-free laws were being achieved as people were reporting on being able to work and socialise in smoke-free environments.
The vast majority of workers (96 per cent) surveyed reported that their workplace was not smoky, while the percentage of those who felt the pub they most recently visited was smoky dropped from 52 to 2 per cent.
