By Kanupriya Kapoor and Fergus Jensen

JAKARTA (Reuters) - Indonesia's president held a cabinet meeting aboard a warship off the Natuna Islands on Thursday, asserting sovereignty over waters in the southern reaches of the South China Sea after Beijing stated its "over-lapping claim" on nearby waters.

President Joko Widodo's visit to the remote island chain along with his chief security minister, foreign minister, and military chief was described by Indonesian officials as the strongest message that has been given to China over the issue.

During the cabinet meeting onboard the Indonesian navy corvette, Widodo called on the military to step up patrols in the wake of a series of face-offs between Indonesian and Chinese vessels in area.

"The capabilities of the military...in securing our seas should be improved, whether it's technology or general preparedness," Widodo said, according to a presidential palace statement.

Officials told reporters the cabinet also discussed matters of sovereignty and development. Indonesia has established a special economic zone in the gas-rich waters around Natuna Islands, which lie over 340 kilometers (212 miles) off the northwest tip of Borneo island.

Cabinet Secretary Pramono Anung, who also accompanied Widodo, posted online photos of the president aboard the warship and of a written message he left for the crew, saying "Defend Indonesia".

The president's visit to a body of water that Indonesia calls the Natuna Sea reflected the government's strong stance over the issue, Chief Security Minister Luhut Pandjaitan said.

"In the course of our history, we've never been this stern (with China). This is also to demonstrate that the president is not taking the issue lightly," he told The Jakarta Post newspaper.

Both sides have denied that the matter represents a territorial or diplomatic dispute.

But, Beijing officials repeated on Thursday that while China does not dispute Indonesia's sovereignty over the Natuna Islands, "some waters of the South China Sea" were subject to "overlapping claims on maritime rights and interests".

"We hope that Indonesia can meet us halfway, objectively recognize the relevant dispute and appropriately resolve the relevant fishing issue to jointly maintain the overall picture of the development of bilateral relations and regional peace and stability," Chinese Foreign Ministry spokeswoman Hua Chunying told a daily news briefing.

(Additional reporting by Ben Blanchard in BEIJING; Editing by Simon Cameron-Moore)