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Ireland had the second highest incidence rate of Covid-19 in Europe just last week but also one of the continent's highest uptake of booster vaccines, which has helped keep the number of seriously ill people well below the previous peak.
"We have weathered the Omicron storm," Martin said in Friday's televised address, in which he said booster vaccines had "utterly transformed" the situation in the country.
"I have stood here and spoken to you on some very dark days. But today is a good day," he said.
The country has been one of the most cautious in the European Union on the risks of Covid-19, putting in place some of the longest-running restrictions on travel and hospitality.
But following advice from public health officials, the government decided that bars and restaurants will no longer need to close at 8 p.m., a restriction put in place late last year when the Omicron wave struck, or to ask customers for proof of vaccination.
Indoor and outdoor venues are also set to return to full capacity, paving the way for full crowds at next month's Six Nations rugby championship.
People will still be required to wear masks on public transport and in shops until the end of February, Martin said.
Ireland's hospitality sector, which has been particularly hard hit by one of Europe's toughest lockdown regimes, welcomed the decision.
"The excitement is palpable," Dublin restaurant Las Tapas De Lola said in a Twitter post in which it said it had seen a surge in bookings in anticipation of the new rules.
RTE radio broadcast bar customers cheering Martin's address.
While the economy recovered rapidly last year, around a third of employers have chosen to defer tax payments and the wages of one in 12 workers are still being supported by a state subsidy scheme set to end in April.
The changes put Ireland back in line with British-run Northern Ireland, which had less severe restrictions over Christmas and agreed to scrap vaccine passes on Thursday and reopen nightclubs next week.