The 20-year-old, named locally as Stuart Butler, was surfing with two friends at Byron Bay, New South Wales, when they got into difficulty in a rip tide.
The Byron Shire News said police were now considering the search to be a “recovery operation”.
It is understood Mr Butler got carried away by the tide at around 11am local time on Saturday.
A member of the public saw the drama unfold and called emergency services.
One of the other surfers, a 26-year-old, was rescued from the water by a local surf club lifesaver on a jetski a short distance away from where they had got into difficulty. He was uninjured.
Another 20-year-old surfer was found by rescuers along the cliff face, clinging to rocks. He had suffered minor injuries.
For almost five hours, searchers, including jet skiers from three surf clubs in the area, a rescue helicopter, a police helicopter, and a jet rescue boat combed the seas for any sign of the Irishman.
Dozens of onlookers also packed onto the headland around Byron Bay lighthouse to look for any sign of him.
The jet ski crews found it difficult to stay in the cold water for any length of time and surf conditions became very dangerous, with strong winds adding to the difficulty of the rescue. Therefore, at around 3.30pm, they were forced to call off the search.
Yesterday morning the operation resumed, this time bolstered by the help of a fixed-wing plane and three helicopters.
However, it was called off again a number of hours later due to the treacherous coastal conditions, with local Surf Life Saving Far North Coast duty officer Jimmy Keogh saying crews would search for the man again today.
The Department of Foreign Affairs here said it has been in contact with members of Mr Butler’s family both in Ireland and in Australia.