New Delhi — The Institute of Public Opinion, run here like the Gallup Poll in the United States, has recorded that the ''most admired country'' in India today is the Soviet Union.
Of the educated couples interviewed in the big cities of New Delhi, Bombay, Calcutta, and Madras, 73 percent said that they admired the Russians for backing India on every possible occasion.
Similarly, 73 percent of the 1,500 people interviewed by the institute replied in the affirmative when they were asked whether they preferred Soviet Union to the United States in terms of its policies and attitudes toward India.
Almost two out of every three persons interviewed said that the Reagan administration's policies were ''dangerous'' to India. Mr. Reagan's attitude toward India and Mrs. Gandhi's government was considered to be ''unwise and unhelpful.''
But individual Americans were admired. Most people wanted India to continue to have good relations with the US as far as its universities, business firms, and other unofficial organizations were concerned.
But the Reagan administration remained the No. 1 topic of dislike.
A Western diplomat, commenting on the poll results, said: ''It is not surprising that Indian public opinion has turned against the US. It is not merely a question of arms supplied to Pakistan. The average educated Indian bureaucrat or businessman has begun to believe that the Reagan administration is giving very low priority to India.''
An American diplomat said privately: ''Perhaps it is a calculated risk we are taking. India is certainly a major power on the subcontinent. But her continued support to the Soviets, despite the Russian occupation of Afghanistan, is a sore point with us. We have failed on the diplomatic front. There is nothing we can do to persuade Mrs. Gandhi to accept our point of view. In fact, she makes every attempt to ignore Americans and bypass Washington whenever she goes abroad.''
Behind the high walls and barbed wires sits the American Club. An armed guard stands at the massive locked gates. No Indian can enter the area, which has a swimming pool and other game facilities for American diplomats, their families, and their guests. Indians can visit this restaurant which is known for its American food, not just hamburgers and fried chicken, as guests of US diplomats.
White-gloved waiters wearing jackets and starched collars hover over the place taking orders. An Indian would feel distinctly uncomfortable except for the fact that his American hosts are more than kind. They are generous.
One says regretfully: ''Time was when the gates of the American Embassy were open to the Indians. They were welcome all the time. Now, we have to impose restrictions. Relations have gone down the drain and we have come to believe that whatever we might do, New Delhi will continue to frown on us.''
Another high-ranking diplomat comments: ''Even if we fire a 21-gun salute for Mrs. Gandhi she would not bother to improve relations with us. She has insisted on believing that the US is pursuing an inimical policy toward India.''
In a recent interview with a London-based correspondent, Mrs. Gandhi pointed out that the Americans are interested in the Soviets continuing to remain in Afghanistan. For the Russians will remain preoccupied with the turmoil in Kabul and the insurgency there.
Western diplomats have also noted that in speech after speech, statement after statement, Mrs. Gandhi harps on the same theme that the US is contributing to the tensions in the subcontinent. Reagan is interfering in the internal affairs of South Asia, bringing war to its very doorstep.
In the face of statements by the prime minister and other officials it is not surprising that the Indian public opinion has been affected by the mounting criticism of Washington.
Western observers believe that even if Secretary of State Alexander M. Haig Jr. had visited India he could not have done much to improve Indo-American relations.
An Asian ambassador, who has watched the Indo-American relations going from bad to worse, says ruefully: ''We find angry editorials in Indian newpapers. A wave of anger is hitting the Western community. And even Asian diplomats are being bracketed as either pro-West or Western stooges. We do not know which way this wave is going to push us.''
The near halting of American aid to India is considered by most observers as a major roadblock toward improving Indo-American relations.
Most Indian officials have concluded that somehow the US government is not interested in improving relations with New Delhi because India is given a very low priority in the scheme of things as Washington sees it.