Data published by the Department of Health reveals 97% of premises inspected in the two weeks after 1 July were smokefree as required by the new law.
Minister of State for Public Health, Dawn Primarolo, said: "All the signs are that businesses and the public have taken the new law in their stride."
So far, data has been collected from nearly 90,000 inspections, which includes 1,090 hotels, 6,783 restaurants and 9,568 licensed premises.
Enforcement officers found that 97% of premises were respecting the requirement to prohibit smoking in enclosed premises and 79% were displaying the correct no-smoking signage.
Department of Health