The ship had 43 crew onboard, including two New Zealanders, when it sank in a typhoon in the South China Sea last week. It had left Napier in August and was carrying almost 6000 cattle.
Families of the New Zealanders - Scott Harris, and Lochie Bellerby - have been pleading with the government to be more actively involved in the search.
In a statement, Minister of Foreign Affairs and Trade Winston Peters said he acknolwedged it would be meaningful for the families to understand what happened "to cause this tragic loss of life."
"That is why officials have been instructed to investigate the viability of searching for the ship's black box - in concert with interested international partners, such as Panama, Japan, Australia, the Philippines and the ship's owners."
Currently, the Japan Coast Guard has been taking the lead in the search for the crew and the vessel, which was registered in Panama. The majority of the crew were Filipino, but there were also two Australians.
Three crew members were found; two were alive but one man was unconscious and later died.
The responsibility went back to Panama to investigate the incident in accordance with established international procedures, Maritime NZ said yesterday.
"We understand that such a search could be difficult and expensive, given the depth at which the ship is believed to have sunk. But we believe it is only responsible to explore what might be possible," Peters said.
"Personal engagement with my counterparts in Panama, Japan, Australia and the Philippines will be made to underline the seriousness with which the New Zealand Government is approaching this matter."
Peters said they were still in close contact with Japanese officials conducting the search and Maritime NZ would continue to provide support to their efforts.
The Japan Coast Guard is conducting routine patrol searches in the area.
In a statement yesterday from Australia's ministry of foreign affairs, they said "Australia is encouraging Japan's ongoing air and sea efforts, and continues to offer the Japanese authorities any supporting capability needed."
