Three crew members were accounted for when they were picked up by a Fijian Navy patrol shortly after the tuna longliner FV Tiro II sank on 21 May.
They were questioned and then released by police earlier this week.
A spokesperson for the Fiji Navy said the search covered an area of almost 8000 square kilometres.
The decision to suspend the operations was not taken lightly.
Earlier Captain Humphrey Tawake told Fiji media the alleged murder took place following a "heated argument" between two Fijian crew members.
