Irish smoking "quitline" has received more than 30,000 calls
Bertie Ahern said it was clear the ban on workplace smoking was having a positive effect.
Since the end of March 2004, smoking has been illegal in workplaces, including pubs and restaurants in the Republic of Ireland.
It was the first country in the world to introduce such a nationwide ban.
Mr Ahern said it had proved a positive effect not only on the health of the nation, "but also on the functioning of our health services".
He was speaking on Friday, marking the Irish Cancer Society's main fund-raising day.
People now recognise passive smoking as a serious health and safety issue and wish to be protected from it
Bertie Ahern
Irish prime minister
"Compliance levels throughout the various sectors have remained consistently high, with overall compliance of 94% being recorded by the Office of Tobacco Control.
"Right across the country, people value being able to work and socialise in a clean and healthy environment," he said.
'Passive smoking'
The government-backed smoking "quitline" has received more than 30,000 calls since it was set up 18 months ago, said the taoiseach.
"It is estimated that 7,000 smokers have given up smoking, with many more reducing their intake of tobacco products considerably.
Mr Ahern said compliance levels remained consistently high
"Not only are smoke-free enclosed workplaces being accepted as the norm, they are also seen as a right.
"People now recognise passive smoking as a serious health and safety issue and wish to be protected from it," said Mr Ahern.
Last year, a major drinks company blamed the smoking ban for a fall in the sales of Guinness.
Shares in Diageo, the world's biggest drinks company, fell by 4%.
Owners of pubs where people are caught smoking illegally by health inspectors enforcing the ban can be fined up to 3,000 euros (£2,400).
A smoking ban in all Northern Ireland government departments came into effect in January.
Many in Northern Ireland, particularly doctors and politicians, have called for a universal ban.
Tomorrow will be an historic day in the Republic of Ireland. It will be exactly one year since the initial introduction of the once controversial . The ban, introduced on March 29 2004, made Ireland the first country in world to completely ban smoking in all workplaces.

The idea was initially met with much skepticism by the Irish who traditionally had a worldwide image as a land of drinkers and smokers. However despite this early uncertainty, the ban has been a huge success. Cigarettes sales have fallen by as much as 60% in , with the country's biggest tobacco brand, , reporting an overall drop in sales of 7.5%.

The   announced earlier this month that over 7,000 had given up smoking in the past twelve months. A survey by the  showed 82% supported the ban. Anti-smoking lobby groups such as ASH had been calling for a ban for many years prior to the Government's initiative.

On 3 December 2003, New Zealand passed the  which lead it to become the second nation to impose a total ban. Its ban came into effect nine months after Ireland's, on 10 December 2004. In January of this year Italy also introduced a ban. Sweden intends to go smoke free in June of this year and in Scotland, the  hopes to have a ban in effect by early 2006.