The annual exercises, called Balikatan, are due to run until 27 April.
This year they are taking place off Palawan, near parts of the South China Sea both Manila and Beijing claim.
Meanwhile Philippine and Chinese vessels remain at the Scarborough Shoal, a week after the deadlock began.
The Philippines said its warship found eight Chinese fishing vessels at the shoal – which both sides claim – when it was patrolling the area on 8 April.
When navy personnel boarded the Chinese fishing vessels on Tuesday they found a large amount of illegally-caught fish and coral, it said.
Two Chinese surveillance ships then arrived in the area, preventing the navy from making arrests.
Incidents in the South China Sea involving fishing boats or energy survey vessels are becoming more frequent, demonstrating the lack of any common rules of the road to resolve competing territorial claims.
China insists that its rights in areas like the disputed Spratly Islands are paramount, despite rival claims from the Philippines, Vietnam and other countries too.
The government in Manila is taking steps to modernise its small naval and air forces. But it is looking to Washington to help balance China’s growing power.