Vittorio Missoni, 58, wife Maurizia, two friends, and two Venezuelan crew were still missing last night more than two days after contact was lost off the resort island of Los Roques.
The Milan-based businessman, who owns the five-star boutique hotel Hotel Missoni, named after the designer label, on the Royal Mile, had been heading back to Caracas from a holiday aboard the BN-2 Islander aircraft.
Rescue teams continued to search over the weekend but there was no trace of the missing party.
Mr Missoni's company yesterday released a statement: "Missoni confirms that Vittorio Missoni and his partner have been lost in Venezuela. The small airplane in which they were travelling has disappeared. This is the only information available at present."
Mr Missoni's younger brother, Luca, who is active in the family-run business, is reportedly travelling to Venezuela to monitor search efforts.
Francisco Paz Fleitas, president of Venezuela's civil aviation agency, said the plane had enough fuel for a three-hour flight. In a statement, the agency said the last known position of the aircraft was about 11 miles south of Los Roques.
Oswaldo Scalvenzi, a relative of Elda Scalvenzi, one of Mr Missoni's friends aboard, said: "We're holding onto a glimmer of hope. Until we can see the wreckage, hope will remain."
The Missoni Hotel in Edinburgh, which opened in June 2009, was the first hotel to be opened by the 60-year-old Italian fashion house. A second has since opened in Kuwait City.
Mr Missoni, whose parents founded the brand in 1953, is credited with reviving the company's fortunes in the 1990s and 2000s, which saw expansions into retail, hotels, and interior decor.