(Reuters) - Amarin Corp Plc can promote its fish-oil pill for unapproved uses after the U.S. Food and Drug Administration decided not to appeal a judge's ruling that the company has the right under the First Amendment to make truthful and non-misleading statements about its products.

In August U.S. District Judge Paul Engelmayer in Manhattan issued a preliminary injunction allowing Amarin to promote the pill, Vascepa, for off-label uses as long as it does so truthfully. Under a settlement reached between Amarin and the FDA, the agency agreed to be bound by the court's conclusion, Amarin said on Tuesday.

The closely watched case is the first to defend the promotion of drugs on First Amendment grounds since 2012. Then, a U.S. court overturned the conviction of drugs salesman Alfred Caronia, who was caught talking to physicians about unapproved uses for the narcolepsy drug Xyrem. The court ruled that the First Amendment protected truthful and non-misleading speech.

Amarin sells Vascepa for patients with extremely high levels of blood fats known as triglycerides. The company also wants to market the drug for patients with high, but not extremely high triglyceride levels.

The Ireland-based company said the settlement "serves the public interest by supporting informed medical decisions for tens of millions of patients with persistent high triglycerides."

Under FDA rules, physicians are allowed to prescribe drugs "off label" any way they see fit but companies are not allowed to promote them for such uses.

"It is important to note that this settlement is specific to this particular case and situation, and does not signify a position on the First Amendment and commercial speech," the agency said in a statement.

Public health advocates fear the ruling could open the door for drug companies to peddle their products for all kinds of conditions for which they have not been tested. Over the past decade drug companies have paid more than $16 billion in settlements for off-label promotion according to the American Medical Association.

A 2012 study showed that up to 75 percent of published pre-clinical trial results could not be reproduced. Another study showed that when scientists attempted to corroborate 34 claims from frequently cited published trials, they were unable to do so 41 percent of the time.

(Reporting by Toni Clarke in Washington; Editing by Matthew Lewis)