Talley's general manager Tony Hazlett said the full details of the incident on Sunday afternoon remained unclear.
However, it appeared Mr Muir had died as a result of "a major and catastrophic gear failure during routine purse seine operations".
Purse seine fishing involves drawing together a net using a purse line.
The Captain MJ Souza - a New Zealand-flagged 68m tuna boat operated out of Nelson -- arrived in Apia, Samoa, this morning.
Mr Hazlett said the vessel was met by Talley's representatives as well as investigating authorities.
"There will be full investigations into all aspects of the accident to establish what has happened and we will comment further once this is known."
Mr Hazlett said the company's first priorities were with Mr Muir's family and crew mates, who were "understandably devastated".
"We are doing everything possible to assist them in this difficult time."
Mr Muir's body would be returned to New Zealand as soon as it had been released by the Samoan coroner.
His family has requested privacy, Mr Hazlett said.