(Adds CEO quote, details about location of shipwreck; updates share movement)

Feb 2 (Reuters) - Shares of Odyssey Marine Exploration Inc (OMEX.O: Quote, Profile, Research) shot up more than 32 percent, after the Florida-based treasure-hunting firm said it discovered the shipwreck of Admiral Sir John Balchin's British warship HMS Victory, lost in 1744.

The British Royal Navy warship has a bronze cannon, and research indicates a substantial amount of gold and silver was aboard, the company said in a statement.

However, the company did not specify the value of its find in the press release. Calls to the company seeking comment were not immediately returned.

Odyssey Marine said it discovered the shipwreck nearly 100 kilometres (62 miles) from where the ship was historically believed to have been wrecked -- on a reef near the Channel Islands.

The company said it is cooperating with the UK's Ministry of Defence (MOD) on the project, and the terms of the collaboration between the two parties are being negotiated.

"Fortunately, this shipwreck is not in waters claimed by any other country, so we do not expect any interference in further exploration of the site," Chief Executive Greg Stemm said in a statement.

Tampa, Florida-based Odyssey has been embroiled in a legal dispute with the Spanish government, after it recovered a shipwreck with gold and silver coins in 2007 and flew the haul -- estimated by some to be worth $500 million -- back to the United States.

The Spanish government claims that the shipwreck was a Spanish warship, and it is the rightful owner of the wreck and precious cargo.

Shares of the deep-ocean shipwreck exploration company rose to a high of $5.23, but later pared their gains to trade up 22 cents at $4.17 Monday afternoon on Nasdaq. (Reporting by Shradhha Sharma in Bangalore; Editing by Pratish Narayanan)