NEW YORK (Reuters) - New York City said on Friday it sued BP Plc for over $39 million of losses it claims beneficiaries of the city's pension funds suffered due to BP's "misconduct and fraudulent behavior" linked to the 2010 Deepwater Horizon oil spill.

"BP failed to disclose to shareowners the serious risks involved in its offshore drilling operation," Comptroller John Liu said. "After the spill began, it misleadingly attempted to minimize the extent of the damage and the cost to shareowners."

The lawsuit, filed in the Southern District of New York, alleges BP failed to disclose facts about the dangers involved in offshore drilling operations, the extent of the leak and the estimated cost of the cleanup costs.

"The estimated transactional investment losses to City pension beneficiaries caused by BP's misconduct and fraudulent behavior exceed $39 million," the Comptroller's office said in the news release.

BP's New York-traded stock was down 0.3 percent at $42.1 after the news, in line with the overall market.

The 2010 disaster in the Gulf of Mexico killed 11 rig workers and spilled 4 million barrels of oil in the worst offshore spill in U.S. history.

BP has estimated it could spend more than $42 billion to cover clean-up, fines and other liabilities. It has been selling a variety of assets to help cover its costs.

A trial for direct damages related to the spill got underway in February. The trial is being held with no jury before Judge Carl Barbier at federal court in New Orleans.

A U.S. civil trial has already been set for August 2014, regarding accusations that BP committed fraud by misleading shareholders before and after the 2010 Gulf of Mexico oil spill about its ability to respond to the accident.

(Reporting by Edward Krudy and Hilary Russ; Editing by Vicki Allen and Andre Grenon)