The latest discovery occurred Monday, when Graeme and Jan Bickley, a couple visiting from New Zealand, happened across a bundle in the water during a morning stroll. Graeme Bickley told the Associated Press that they had heard about the body parts and joked about it when they saw the bag tied with a nylon line.

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He approached the water to have a closer look, quickly realizing that they had spoken too soon.

"I scrambled in and grabbed hold, it was very, very heavy," Bickley said. "I dropped it on the sand and you could hear there were rocks in it. I looked at the shape of it, and thought 'This isn't looking good.'"

The shape turned out to be that of a severed head.

Fiji police believe the head, along with severed feet and a decomposed body found on Natadola previously, belong to Yuriy Shipulin and Nataliya Gerasimova. According to the Fiji Sun, the couple moved to Fiji from Russia five years ago, and ran a farm growing fruits and vegetables that they sold to local businesses.

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They went missing on June 16, after last being spotted having drinks on Denarau Island. The following day, police found the couple's vehicle unattended with the keys still in the ignition.

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A business partner, Andrew Luzanenko, told the Sun that Shipulin and Gerasimova had been struggling financially since their farm was hit by a cyclone earlier in the year.

In a statement on Tuesday, local authorities said no more will be divulged about the case until the investigation is completed. The Fiji military and navy are combing the waters by Natadola, and Interpol has been called in to assist.

A police official told the Sun on Wednesday that they have some leads, but did not give more details.

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In the statement, the public and media were advised at length to refrain from conjecture, so as not to taint Fiji's reputation:

I want to urge members of the public not to speculate or spread unsubstantiated rumours about the case as it only serves to create unnecessary fear...Fiji remains a peace loving country and like other countries, crimes of serious nature do happen because there are elements in society that involve themselves in these type of activities...Speculation as such can paint a negative image of what's happening in Fiji.

Acquaintances of the couple who spoke to The Guardian were troubled by the developments.

Shafia Hassan, a businesswoman who worked with Shipulin, remembered him as "gentle and helpful" and his wife as a "soft, kind lady."

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"This case is a huge mystery for us," Hassan said. "It is all we can talk about because there are still pieces of the bodies to be found. Whoever did this is mad."

The U.S. State Department's Bureau of Diplomatic Security described Fiji as "the hub of the South Pacific Region" and gave the island country a high crime rating in a 2015 report.

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While Fiji's tourists have not been disproportionately affected by crime, the report said, "foreigners attract more attention than local citizens and are perceived to carry more money and, therefore, have been targeted in armed and unarmed robberies and assaults."