Hubertus Keil, 74, and his wife Birgid, 71, had been visiting Tobago, part of the twin island nation of Trinidad and Tobago, for the last 15 years and were well known locally, the Tobago House of Assembly said in a statement published on Sunday (local time).
"Their deaths come as a shock to all of Tobago," the statement added, noting that crime locally was on the decline.
"The police have already set up a high-level team to pursue the investigation, with the aim of bringing to justice whoever is responsible for the Keils' deaths," it said.
Media reports said the bodies appeared to have suffered chop wounds. Police said the couple arrived on Oct. 25 and had been staying at their home in Bacolet on the southwest coast.
They were last seen alive on Friday evening. Police said a gardener arrived at their home on Saturday morning and when he could not find them, went to a nearby beach, where he discovered the body of Birgid Keil. The police were called and the second body was found nearby on the beach.
The murders recalled another double slaying in Tobago in 2008 of an elderly Swedish couple, 73-year-old Ake Olsson and his 62-year-old companion Anna Sundsval. Their mutilated bodies were found in a villa which they owned.
Tobago, with a population of 60,000, is a popular holiday destination for Europeans, particularly Germans and British.