NEW DELHI, JAN. 2 -- A kidnaping by rural left-wing extremists known as Naxalites has seriously embarrassed Indian officials and has drawn attention to one of the country's most intractable social problems.

More than two dozen officials, including eight members of the elite Indian administrative service, were kidnaped Sunday night in a remote region of Andhra Pradesh State. They were released later in the week after state officials capitulated to a demand for the release of seven Naxalites imprisoned for killing several policemen.

Newspaper editorials noted that the state government had little choice but to give in to the militants' demands, given their demonstrated ruthlessness. But the federal government in New Delhi, facing a host of groups with grievances, quickly made its displeasure known.

"There can be no compromise with such violence and there can be no appeasement of terrorism," a government spokesman said here. "The government would like to warn all terrorist and extremist elements in the country that such acts will be met with the strongest countermeasures."

In Andhra Pradesh, a large state in central and southeastern India, the Naxalite movement has been a serious problem for more than two decades. The group, also known as the Communist Party of India Marxist-Leninist, gets its name from an uprising in a place called Naxalbari in West Bengal in the late 1960s when militants, drawing on their interpretations of Mao Tse-tung's tactics in China, began to fight for changes in the inequities of Indian rural life.

Officials in New Delhi, faced with militant uprisings by Sikhs in Punjab, Gurkhas in Darjeeling, disaffected tribal nationalists in the northeastern part of the country and other rural-based militants in Bihar and Maharashtra states, clearly fear that others would take note of the kidnapers' achievement in Andhra Pradesh and the country could face a rash of similar incidents.

Also at issue is the sharp political division between Prime Minister Rajiv Gandhi's Congress (I) Party, in control in New Delhi and about half the country's states, and the regional party of Chief Minister N.T. Rama Rao in Andhra Pradesh.

The incident underscored the serious policy differences that can emerge under India's federal structure.

Under the Indian constitution, police matters are under the control of the states. When a state government is run by the same party as the central government, it is relatively easy to harmonize policies. When a state is ruled by a rival party, however, harmony on crucial questions such as the response to kidnapings depends on the willingness of the political leaders to cooperate. The Gandhi government and Rama Rao, a former Telegu language film star turned politician, are not on good terms.

The Naxalite kidnaping is not the only major issue in which federal-state divisions have played a major role.

Apparent differences between New Delhi and the West Bengal government of Communist leader Jyoti Basu have complicated the approach to the Gurkha uprising in Darjeeling.

In Punjab, the center of violent Sikh nationalism, the government in New Delhi finally took direct control of the state under a constitutional provision known as president's rule.

In West Bengal and Bihar states, Naxalites have recently been involved in confrontations between landless peasants and feudal landlords, although the grievances of India's indigenous tribal groups also have played a major role. In Andhra Pradesh, the movement generally has been based among tribes that inhabit the hill country and forests stretching across the northern rim of the state.

The tribal peoples of India, generally even less educated and poorer than the poorest Hindus, have had few places to turn for help as a burgeoning population has encroached on their traditional forest and pasture lands.

The Naxalites are believed to have received some Chinese support in the 1960s and perhaps early '70s, but have never been a major threat nationally. In West Bengal, the generally independent Communist Party of India Marxist has preempted them and the Soviet-aligned Communist Party of India is also a rival.

The Naxalites, nevertheless, seem to have carved out a small but determined following in some of the country's most depressed rural regions.

There are believed to be about 500 Naxalite activists in Andhra Pradesh, mostly armed with old rifles, pistols and some home-made weapons, including crude hand grenades. They are said to have the backing of about 5,000 active supporters.

The group that carried out this week's kidnaping, the People's War Group, is known as the most militant, and is headed by Kondapalli Seetharamaih. It is said to be organized in small dalams, or armed groups, with bases in the jungles of Nizamabad, Adilabad and East Godavari districts. More than 50 such dalams belonging to a half dozen splinter groups are reportedly operating in Andhra Pradesh and officials hold them responsible for the deaths of 62 people, including 24 policemen, during 1987. Government response to the Naxalites has fluctuated between harsh police actions and proposals to improve the lot of the landless poor and the tribal groups that provide their base.