Owners of the Duzgit Venture have admitted it could have "trapped" Tonga's internet cable with an anchor in January.
The incident, which left Tonga with drastically cut internet services for 12 days, has been described by Tonga's internet provider as sabotage.
A shipping manager with the Duzgit Venture's local agent, Dateline Shipping, said he's handed over vessel data to the police.
But Fine Tohi said the tanker is still servicing Tonga and made a delivery on Wednesday.
"We are the agents of the ship, of that oil tanker and we are still the agents for her as she continues to service Tonga and bring their oil from Fiji."
Police didn't immediately respond to requests for comment on the status of their investigation.
Satellite data placed the Duzgit Venture at the locations and time of the cuts to Tonga's only international undersea internet cable link on January 20, according to the director of Tonga Cable.
Paula Piukala told RNZ Pacific in July it "was clearly sabotage" by a powerful but unknown actor.
Weeks after the incident, the Turkey-based Duzgit told the French oil giant Total - whose oil the Venture was carrying at the time of the cable cut - that it could have "trapped a cable with its anchor", a Total spokesperson told RNZ Pacific last month.
Duzgit has declined to comment while the police investigation is ongoing.
Tongan officials have said they will pursue damages against anyone responsible for the cable cut.