The proposal was the latest in a series of United States overtures to India, a country wary of forming strategic alliances, to become part of a network of naval powers that would balance China’s maritime expansion.

The American ambassador to India, Richard R. Verma, expressed hope in a speech that “in the not-too-distant future,” joint patrols by navy vessels from India and the United States “will become a common and welcome sight throughout Indo-Pacific waters.”

And officials have said that the United States is close, after 10 years of demurral from the Indian side, to concluding a logistics agreement that would allow the two countries’ militaries to easily use each other’s resources for refueling and repairs.

Though he did not specifically mention China on Wednesday, Admiral Harris said powerful countries were seeking to “bully smaller nations through intimidation and coercion,” and made the case that a broad naval collaboration was the best way to avert it.

“Exercising together will lead to operating together,” he said, before meetings with his Indian counterpart. “By being ambitious, India, Japan, Australia and the United States and so many like-minded nations can aspire to operate anywhere in the high seas and the airspace above it.”

Since Prime Minister Narendra Modi took office, India has ramped up naval cooperation with the United States. It reacted angrily in 2014 when a Chinese People’s Liberation Army submarine docked in the Sri Lankan port of Colombo, and has warily watched the expansion of one of President Xi Jinping’s priority projects, a maritime “silk road” with major ports in Gwadar, Pakistan, and Chittagong, Bangladesh. When President Obama visited India last year, the two countries issued a joint statement on “the Asia-Pacific and Indian Ocean region,” something India had refused to do in the past.

Still, some of the American proposals smack of wishful thinking. India has not, to date, shown interest in carrying out joint patrols with the United States, even under the more neutral auspices of counterpiracy operations.

Officials here rebutted a Reuters report last month in which a United States official suggested India might participate in joint patrols in the South China Sea, something not even treaty allies like Australia or Japan have agreed to.

“The last thing India wants to do is accidentally make itself into a front-line player in the South China Sea,” said Nitin A. Gokhale, a security analyst, adding that “the best U.S.-aligned players can expect” is for India to remain active in regional forums, and shore up smaller navies like those of Vietnam and the Philippines.

“I don’t think India will be a front-line state,” he said.

Admiral Harris’s proposal of a quadrilateral security grouping, given at a forum hosted by the Observer Research Foundation, is certain to capture Beijing’s attention. It did the same in 2007, when Prime Minister Shinzo Abe of Japan introduced the idea.

But Chinese analysts viewed the grouping as hostile; one called it a “mini-NATO.” Even before the four countries convened for their first joint meeting, China had sent formal diplomatic protests to Washington, New Delhi, Canberra and Tokyo. At a summit meeting with China less than two years later, Australia announced that it was withdrawing from the quadrilateral arrangement.

Under Mr. Modi, India’s navy has embarked on the creation of a web of bilateral and trilateral agreements, which serve the same purpose but are less likely to be “caricatured” by China as a containment strategy, said Rory Medcalf, the head of the National Security College at the Australian National University. He added, however, that growing cooperation with the United States had forced China to take India more seriously.

Shen Dingli, a professor of international relations at Fudan University in Shanghai, dismissed the idea that the grouping could be revived, and said that India would not join such a network for fear of Chinese retaliation.

“China actually has many ways to hurt India,” he said. “China could send an aircraft carrier to the Gwadar port in Pakistan. China had turned down the Pakistan offer to have military stationed in the country. If India forces China to do that, of course we can put a navy at your doorstep.”