GENEVA/WASHINGTON, April 14 (Reuters) - The United States must do more to fix its dolphin-safe labels for canned tuna after losing a trade dispute with Mexico, the World Trade Organization said on Tuesday.

The United States revamped its labeling rules two years ago after a WTO finding in 2012 that the rules discriminated against Mexico, but the WTO said they still showed less favorable treatment of Mexican tuna than that from other countries.

"We recommend that the dispute settlement body request the United States bring its measure, which we have found to be inconsistent with (the WTO rules) ... into conformity with its obligations," the WTO panel said in its final report.

The ruling potentially opens the door to Mexican retaliation against U.S. imports. The United States can also appeal, as it has in a dispute with Mexico and Canada over beef labeling, or agree on a settlement with Mexico to end the case.

Mexico has been fighting for more than 20 years over rules the country argues have frozen its fishing industry out of a U.S. imported canned tuna market worth $680 million in 2014 by preventing Mexican tuna from carrying a dolphin-safe label. Mexico has about a 3.5 percent market share.

The clash stems from the fact that yellowfin tuna swim with dolphins in the eastern tropical Pacific, where Mexico's fleet operates, using speedboats to herd the dolphins and large purse seine nets to catch the tuna swimming beneath them.

Millions of dolphins were killed before international conservation efforts set standards to protect dolphins and put professional observers on ships to record each tuna catch.

Mexico argued the agreements cut dolphin deaths to minimal levels - below the thresholds allowed in U.S. fisheries - and that tuna from other regions does not face the same stringent tests, with ship's captains allowed to self-certify that no dolphins were harmed.

But the United States argued it was reasonable to make distinctions between products based on fishing methods and said Mexico had not shown any cases of a ship's captain lying about whether dolphins had been killed while catching tuna.

The panel found the different certification standards and tracking and verification requirements, although provisionally justified for conservation reasons, were not even-handed. (Reporting by Tom Miles and Krista Hughes; Editing by Bill Trott and Jonathan Oatis)