OSLO (Reuters) - Most coral reefs in the Caribbean could vanish in the next two decades, hit by the loss of fish and sea urchins that eat a slime of coral-smothering algae, a U.N.-backed study said on Wednesday.

The review, the most comprehensive to date of Caribbean reefs that are vital tourist attractions for many island nations, said climate change had played only a minor role in the reefs' demise, despite past speculation it was a main cause.

"With only about one-sixth of the original coral cover left, most Caribbean coral reefs may disappear in the next 20 years, primarily due to the loss of grazers in the region," according to the study by 90 coral experts.

Bright-colored parrotfish and sea urchins are the two main grazers on algae - microscopic plants that can choke polyps, the tiny animals that build reefs with their stony skeletons.

Over-fishing of parrotfish and a mysterious 1983 urchin disease had let algae thrive in the region.

Still, the study said recovery was still possible, with restrictions on fishing and pollution. Tourism accounts for about 14 percent of gross domestic product in Caribbean economies.

"Caribbean reefs are not a lost cause," Carl Gustaf Lundin, director of the global marine and polar program of the International Union for Conservation of Nature (IUCN), told Reuters.

Some of the healthiest reefs had big populations of parrotfish, including off the United States in the northern Gulf of Mexico, Bermuda and Bonaire, the study said.

All had "restricted or banned fishing practices that harm parrotfish, such as fish traps and spearfishing. Other countries are following suit," it said.

And climate change was still a threat because corals struggle in warmer, more acidic seas. But the report showed that many measures could be taken locally, without waiting for other nations to cut greenhouse gas emissions.

(Reporting By Alister Doyle; editing by Keiron Henderson)