Lochie Bellerby was one of two New Zealanders among the 43 people who were on the cattle ship Gulf Livestock 1, which capsized during a typhoon last week.
Three people from the ship were found last week, only two of whom survived.
ABC is reporting that the Japanese Coastguard overnight made the decision to suspend its full-time search for the 40 people still missing from the ship.
Authorities say they will now only look for survivors as part of their regular patrols in the area.
Mr Bellerby's family said in a statement this morning they understood why the search for their missing son had to be scaled back given the area he went missing in was such a busy shipping area.
''We understand local search and rescue teams remain in the area as the country responds to the aftermath of the typhoons.
However, they were still hopeful Mr Bellerby would be found.
''Lochie is a very capable and strong person both physically and mentally.''
The family yesterday acknowledged the kindness and consideration shown by the Ministry of Foreign Affairs and Trade, Maritime New Zealand, New Zealand Police and Interpol, as well as "the effort and dedication of the Japanese Coastguard, the caring support of family and friends, and of the local community during this challenging time".
The family were looking forward to Mr Bellerby’s brother and his brother’s Canadian partner arriving home in New Zealand.
Family spokeswoman Sue Sherburd said last night Mr Bellerby had visited his family before travelling to Napier to board the ship, which left on August 14.
Meanwhile the family of the other New Zealander missing, Scott Harris, 37, from Palmerston North were disappointed at the news.
Harris' mother, Karen Adrian, told RNZ she was devastated to hear the search had been called off, and there was nothing she could do.
