NEW DELHI — The statement, on its surface, seemed like any other bland missive released at the end of a polite visit by a head of state. It was put out by the United States and China after President Obama’s visit there, and said that the two countries would “work together to promote peace, stability and development” in South Asia.

But on the eve of a visit by the Indian prime minister, Manmohan Singh, to the White House, where on Tuesday he will be the guest of honor at Mr. Obama’s first state dinner, the words rank as one of several perceived slights that have dampened hopes for a new chapter in the sometimes rocky relationship between the United States and India.

The vague statement has been widely interpreted here as an invitation to China to meddle in India’s backyard, and prompted howls of dismay across the political spectrum.

“How can you make China responsible for keeping peace in South Asia?” said Prem Shankar Jha, a newspaper and magazine columnist, channeling the prevailing sentiment among New Delhi’s political analysts. “China has done nothing in South Asia except to play a destructive role here,” he continued, referring to China’s close ties to India’s archrival, Pakistan.

Beyond the surface issues, however, lies a deeper tension, in which India sees a warmer relationship between Washington and Beijing under the Obama administration as a threat to its own rise as a global power, and worries that India is being relegated to a regional role on par with its troubled neighbors Afghanistan and Pakistan.

“There is a feeling that in Obama’s international calculations, India is not that important,” said Lalit Mansingh, a former foreign secretary and ambassador to Washington. “The suspicion is building up that Obama is not as keen on the strategic partnership with India as George W. Bush was. There is, underneath the surface, a suspicion that the Americans are scared or too dependent on the Chinese.”

Mr. Obama’s declining to meet the Dalai Lama in Washington last month was also seen as evidence that he was unwilling to offend China, never mind that India barred foreign journalists from covering the Dalai Lama’s visit to a disputed Indian province in part to mollify China, which opposed the visit.

India and the United States grew closer than at any time in their history during Mr. Bush’s presidency, spurred in large part by a pact on nuclear technology that tacitly legitimized India’s nuclear weapons program and will allow India to import technology to build much-needed nuclear power plants. The Bush administration saw democratic India as a natural counterweight to a rising autocratic China.

The Obama administration has been received more coolly. While Mr. Bush saw India as a singular and vital ally, Mr. Obama “has tended to use Pakistan as the fulcrum of South Asia, and sees India as one knotty strand in the Afghanistan tangle,” said a disapproving editorial in the newspaper Indian Express on Monday.

Indeed, with the United States mired in the Afghan war, and with Pakistan’s growing chaos increasingly inseparable from the Afghan morass, India worries that it will once again become merely a variable in a very complicated regional equation.

In this context, what is seen as American reluctance to confront China on tricky issues has created the impression that the United States worries more about its pragmatic interests with China, to which it owes $800 billion, than standing up for the values it shares with India, analysts and former diplomats here said.

“His bowing before the emperor of Japan was an act of courtesy,” Mr. Mansingh said. “But his bending over backwards before the Chinese was an act of appeasement.”

These tensions in many ways predate both Mr. Bush and Mr. Obama. India and the United States would seem to be natural allies — both are vast, multiethnic and religiously diverse nations that embraced democracy after throwing off the British colonial yoke. Indeed, the United States was an early supporter of Indian independence.

But the relationship has always been rocky, and has foundered on precisely the same grounds: India’s prickliness at being seen as anything but a singular nation with a unique destiny. Cold war politics put the United States solidly on the side of Pakistan. India, under its first prime minister, Jawaharlal Nehru, was officially neutral in the cold war but had socialist leanings and a cozy relationship with the Soviet Union. But India chafed at being defined by these ideologies.

Obama administration officials have taken pains to paint the United States-India relationship as essential and to be respectful of India’s separate path.

“The U.S.-Indian partnership is one of the real keys to global order and global prosperity in the 21st century,” declared William J. Burns, under secretary of state for political affairs, in a statement released after he visited India last month.

Hillary Rodham Clinton, the secretary of state, went on an extensive visit to India in July, making a point of visiting Mumbai and staying at the Taj Palace Hotel, which was attacked by Pakistani terrorists last year.

Prime Minister Singh himself sought to play down any disenchantment with the new administration.

“I have no apprehension that our relations with the United States would in any way suffer because of the change of administration,” he told CNN’s Fareed Zakaria on Sunday, and repeated his oft-stated view that “India and China are not in competition.”

China, meanwhile, has signaled that it has no intention of playing a role in mediating India’s longstanding quarrels with Pakistan. And despite the joint statement issued at the end of Mr. Obama’s visit, it has not expressed any interest in getting involved in Pakistan’s domestic troubles.

Indeed, the relationship between India and the United States encompasses so many spheres that it is difficult to imagine any serious rupture, analysts said. Beyond billions of dollars in trade, there are millions of Indians and people of Indian origin in the United States.

Since the attacks in Mumbai last November, cooperation between Indian and American intelligence and law enforcement agencies has been growing, with each side providing the other with vital information on terrorist threats and networks.

Salman Haidar, a former Indian foreign secretary, said that the natural alliance between India and the United States, frustrated for so long by historic events, is now too strong to be shattered by perceived blunders.

“The exchanges till now between Obama and Manmohan Singh have been very cordial and pointed toward mutual appreciation and respect,” he said. “I think that there is a comfort level that has not been disturbed.”