The trio, aged 25, 27 and 30, were last seen leaving Betio Island, the largest town of Kiribati's capital island of South Tarawa, aboard a 4.5m wooden boat about 3am on Monday.
They were expected to return home later that day.
The men had 56 litres of fuel, a bucket of water and 20 buns with them, according to Fiji's RCC.
Fijian and New Zealand authorities will scour 34,300sq km during the search effort.
A local radio station urged nearby vessels to also keep an eye out for the missing men.
The mission echoes one the NZDF was called to on October 18 to help search for three Kiribati fishermen who had been missing for four days.