GENEVA (Reuters) - Vietnam has challenged U.S. anti-dumping measures against Vietnam's exports of fish fillets, a filing published by the World Trade Organization showed on Friday.

Vietnam says Washington has broken WTO rules in the way it has imposed punitive tariffs on Vietnamese fish it claims are being "dumped, or sold at an unfairly cheap price, on the U.S. market.

U.S. imports of fish fillets from Vietnam have grown from $100 million in 2007 to more than $520 million in 2016. That made Vietnam the third-biggest U.S. supplier after Chile and China and the U.S. the top export market for Vietnamese fish.

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The United States has 60 days to settle the complaint, or Vietnam could ask the WTO to adjudicate.

Washington has faced a slew of trade disputes over its use of anti-dumping duties in the past two decades, and has lost many of them after its calculation methods were found to be out of line with WTO rules.

Earlier this week, the WTO published a wide-ranging Canadian trade complaint, lodged in December, against the U.S. use of anti-dumping and anti-subsidy tariffs.

The United States called that complaint a "broad and ill-advised attack" that could cause a "flood of imports from China and other countries".

The Vietnamese complaint was the fourth dispute initiated by Vietnam since it joined the WTO in 2007.

Two of its previous complaints took aim at U.S. anti-dumping actions against Vietnam's shrimp exports. The long-running shrimp battle finally ended in 2016 when the United States agreed to remove duties on a Vietnamese shrimp exporter and to refund duty deposits that it had paid.

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At the time, the two countries were partners in the Trans-Pacific Partnership trade talks. But under President Donald Trump the United States has withdrawn from those negotiations.

(Reporting by Tom Miles; Editing by Larry King)