Missoni was travelling on board a private jet which vanished off the coast of Venezuela on 4 January (13), and his relatives have been urging local search and rescue teams to continue their efforts until he is found.
They have also launched an online campaign to gather information about what could have happened to the fashion mogul.
It had been feared Missoni bosses would call off the brand's scheduled Milan Fashion Week catwalk show in light of the family's troubles, but they refused to cancel the event and unveiled the company's autumn/winter designs as planned on Sunday.
The show was a pared down affair and Missoni's sister Angela, the brand's chief designer, decided against taking a bow on the runway.
Angela said in a statement, "In this difficult moment for my family and our company, the firm must carry on its business... I can only say that searches will continue in all possible directions until we find them."
Another designer, Donatella Versace, who was also showing her latest collection in Milan, addressed the Missoni family's ordeal before her own show on Saturday (12Jan13).
Versace, whose designer brother Gianni was murdered in 1997, told reporters, "No one better than me can understand the pain and anguish that they are experiencing."