Jonathan W Greenert told reporters on Friday in response to a question about US-India military-to-military ties as Biden embarks on a trip to highlight US policy rebalance towards the Asia Pacific.
The US exercise programme with India called "Malabar", he noted "has gone from two ships going by doing flashing light and lifting flags, probably about a decade ago, to coordinated operations, carrier air wing and under sea".
"And that's when you hit the big time, when you can work with a partner under the water and ensure you're not going to run into each other, and we are at that level with the Indian navy," Greenert said.
However, the admiral acknowledged that the exercise had been downscaled somewhat due to some unexplained issues on both sides.
"So that exercise retains itself," Greenert said. "We had to de-scope it some, because of each of our issues, but we've kept the exercise and we've kept it as high-end and complex."
"It just may not run as long. So I'm comfortable at that level, and we try to work to the level that resonates with both our navies," he said.
On the relations between US and Chinese navies, the admiral said: "I like the trend we're on right now and working toward and, in some cases, getting some tangible outcome of working together."
China, he said, had brought a hospital ship to an exercise hosted by Brunei in June where they "operated together a humanitarian assistance, disaster relief scenario, doing command-and-control together, doing the proper protocols at sea".
"And we agree, this needs to continue," Greenert said,noting China was going to join RIMPAC, Rim of the Pacific '14 exercise that was joined by 22 nations previously.
His counterpart in the Chinese Navy admiral Wu Shengli would be visiting Washington in September "to share insights on things".
"So we want to keep that momentum going," he said.