A joint team of navy and police officers took the men into custody during a pre-dawn operation outside Colombo as they tried to board a fishing trawler, spokesman Chaminda Walakuluge said.
Sri Lankans have sought asylum in New Zealand in the past, most of them members of the island's Tamil minority who say they are fleeing persecution at home.
"The information we have is that they were trying to go to New Zealand," Walakuluge told AFP.
"We handed the men to the police for further action while we look for the people smugglers involved."
Later that same year, 37 people were arrested outside Sri Lankan waters after being turned back by Australia's coastguard.
Breaking the immigration law carries a maximum penalty of two years in jail.
The authorities have also prosecuted dozens of people for organising illegal boat trips, including several naval personnel.
There have been allegations of official collusion with the smugglers during the former regime, which was voted out in January 2015.
Most Sri Lankan asylum seekers have headed for Australia in the past, but Canberra has tightened its refugee policy and those trying to reach Australia by boat are now turned back or sent to remote Pacific island camps.
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