Washington wants to discuss security issues, specifically the South China Sea, North Korea, and Taiwan.
India, in turn, is pushing into the South China Sea, and seeking port facilities in Vietnam.
Both sides ignored shouted questions from reporters about the South China Sea, AFP news agency said.
Do you have a view on China and ASEAN and the South China Sea issues?
Invariably, the leaders will also discuss problems caused by competing sovereignty claims in the South China Sea.
Both countries are locked in a dispute over ownership of resource-rich islands in the South China Sea.
But offshore deepwater exploration could yet produce considerable finds more handily placed in the South China Sea.
But shipping chips across China is not so different from shipping them across the South China Sea.
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Another area of dispute is the South China Sea, which Beijing claims almost entirely as its own.
Her high-profile challenging of Chinese territorial claims in the South China Sea, beginning in 2010, infuriated Beijing's leadership.
In addition, that country and its southern neighbors have sparred over territorial rights in the South China Sea.
The Chinese government has made a positive contribution to safeguard the navigation security in the South China Sea.
Macau sits on a horn of rocky coastline, where the Pearl River washes into the South China Sea.
That should not be hard nearly a quarter of the world's ocean freight passes through the South China Sea.
Onto the coastal borders: the Taiwan Straits, the Bohai Bay, the East China Sea and the South China Sea.
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China says it fired flares, not weapons, at a Vietnamese fishing boat in the South China Sea last week.
BBC: China 'fired flares' at Vietnam boat in South China Sea
Threats of international conflict flickered around and across the South China Sea.
One Western diplomat says he sees its deployment as potentially useful for settling scores in the South China Sea.
We looked forward to the early conclusion of a Regional Code of Conduct in the South China Sea (COC).
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China's claim in the South China Sea is by far the largest, and includes the Spratly and Paracel archipelagos.
For years, China has been making illegal claims to and occupying various contested islands in the South China Sea.
North-east of the South China Sea lies a small crop of islands that Japan and China are squabbling over.
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Other countries in the region believe China also wants to assert territorial claims in the South China Sea more vigorously.
In recent months, China has been facing off against India and Vietnam over activities in the South China Sea.
The Chinese navy "are determined to safeguard the country's sovereignty with their services on the South China Sea", said Xinhua.
BBC: China 'fired flares' at Vietnam boat in South China Sea
That could include running longer and more sophisticated sea and air missions to assert sovereignty over the South China Sea.
"China has made it clear the South China Sea disputes should be solved at the bilateral level, " the editorial says.
Officials said the Washington is deployed in the East China Sea and the Stennis is in the South China Sea.
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