A Russian couple from Fiji are thought to have been murdered and dismembered after human body parts washed up on a beach in the Pacific island nation.

The Fiji Sun said two pairs of feet wrapped in netting and weighed down with stones were found on June 24 at Natadola beach, a popular tourist destination.

Further searches uncovered more remains, with speculation connecting the grisly find to the disappearance a week earlier of Russian couple Yuri and Natalia Shipulin.

Lead investigator Luke Navela said DNA tests with the Shipulins' relatives back in Russia had confirmed the link, and police now believed they had been murdered and dismembered, the Sun reported.

Citing police sources, the newspaper said detectives had information a chainsaw was missing from the couple's farm on the main island of Viti Levu.

The Fiji Times reported that the couple moved to Fiji in 2011 and were leasing the farm and operating a photography business.

A friend, fellow Russian Alla Mallerich, described the pair as "soul mates".

"Yuri was a happy, easy going man who loved life, loved Fiji and he had plans to build his life in Fiji," she told the newspaper.

Social media pictures show a middle-aged couple smiling while drinking cocktails and beers in the sun.

However, their business partner Andrew Luzanenko told the Fiji Sun in the days after their disappearance that they had financial difficulties after the farm was devastated by Super Cyclone Winston earlier this year.

Luzanenko, who also lived at the farm after moving from Russia earlier this year to co-manage it, said the couple left "without even speaking to me".

The investigation is continuing, with navy divers on Monday scouring waters off Natadola beach looking for more remains.