Golf's four leading male players will be missing from the sport’s long-awaited return to the Olympics after world No3 Jordan Spieth became the latest high-profile withdrawal on Monday.
Golf’s leading women are all set to play in Brazil and International Golf Federation president Peter Dawson suggested some of the men had been unnecessarily cautious.
“Personally I think there’s been something of an over-reaction to the Zika situation,” he said.
“But we remain confident we will stage two very exciting and compelling golf competitions in Rio.
"We have all of the top women playing and I think the count is eight out of the top 15 men are going to be playing, so we’re going to have strong fields.”
Golf is back on the Olympic schedule this year for the first time since 1904.
Zika has been linked to defects in newborn babies and the rapid spread of the virus across South America prompted calls for the Olympics be moved or cancelled.
But the World Health Organisation has chosen not to recommend restrictions on travel to any of the Games locations and the International Olympic Committee (IOC) on Monday said the cooler climate in August should minimise the threat of mosquito-borne infections.
Two-time Major winner Spieth will play alongside England’s Justin Rose and Ireland’s Shane Lowry in the opening two rounds of the Open, which starts at Royal Troon on Thursday.
Masters winner Danny Willett is in a group with world No1 Day and No6 Rickie Fowler, while McIlroy tees off with world No5 Bubba Watson – the highest-ranked man set to play at the Olympics – and Japan’s Hideki Matsuyama.