Soviet President Leonid Brezhnev issued a new appeal to China today to resume the search for improved bilateral relations on the basis "of common sense, mutual respect and mutual advantage."

His remarks in a nationally televised speech appeared to be the most positive in a series of recent overtures to Peking. Diplomatic analysts here linked their timing to the scheduled visit to Peking next month of Soviet Deputy Foreign Minister Leonid Ilyichev for preliminary discussions expected to lead to the resumption of Sino-Soviet negotiations.

The 75-year-old Soviet leader's speech at a political meeting in Baku, the capital of Soviet Azerbajian, was marred when Brezhnev began reading the wrong speech.

Appearing vigorous and in good health, Brezhnev was more than a minute into his speech when his personal aide, Andrei Alexandrov, was seen rushing to the rostrum with another text. With cameras turned away from the rostrum, the Soviet leader interrupted his speech to be given the correct text.

Displaying good humor that provoked a thunderous applause from a few thousand persons in the audience, he said before resuming his speech: "It is not my fault, comrades. I have to start again from the beginning." He switched to the new text, which contained somewhat different opening remarks.

In contrast to an appeal he made to Peking in March when his proposal for improved Sino-Soviet relations was coupled with criticism of China's "distortions of the principles and essence of socialism," today's remarks contained no suggestions of the invective that has been standard since the two nations drifted apart over ideology, territory and other issues.

The Chinese have treated the planned visit in a low-profile manner, Washington Post correspondent Michael Weisskopf reported last week from Peking. According to European diplomats there, Ilyichev will be a private guest of the Soviet ambassador to China. Sources said they did not expect any talks between Ilyichev and the Chinese to deal substantively with major issues separating Moscow and Peking.

Asserting that "we do not hold that detente can and must be" confined to any single area of the world, Brezhnev said in his speech that "there exist possibilities" for detente in Asia and that they should be explored intensively.

"We would deem it very important to achieve a normalization, a gradual improvement of relations between the Soviet Union and the People's Republic of China on a basis that I would describe as that of common sense, mutual respect and mutual advantage." He added that this would strengthen peace in Asia and "all the world over."

Brezhnev singled out Europe as the region where detente "for a number of historical reasons had struck deeper roots than in other" areas. But in an allusion that appeared to reflect Moscow's concern about the breakup of the West German ruling coalition and the prospect of a right-of-center government in Bonn, he asserted that detente "in no case must be put at the mercy of the narrow-minded egoistic politicians in the camp of imperialism."

Although there have been no public assessments about the recent developments in Bonn, the Soviets are described by well-informed diplomatic sources as being very worried about the collapse of the Social Democratic-dominated government of Chancellor Helmut Schmidt.

The Soviet leader made no mention of Soviet-American relations or the Middle East situation.

The apparent high priority Moscow attaches to the resumption of Sino-Soviet normalization talks, which were broken off by China following the Soviet invasion of Afghanistan, was seen by diplomats here as being partly based on positive Soviet assessments of the recent Chinese Communist Party congress.

Soviet commentaries have stressed that the Chinese leaders did not rule out the possibility for better relations with Moscow but that "not words but deeds are important" to create conditions for better ties.

The resumption of dialogue was not likely to wipe out quickly the bitter resentments accumulated during the past two decades. But the Soviets apparently hope that this will relieve pressures on Moscow and help it influence its relations with the United States.

Moscow and Peking had conducted border negotiations for almost a decade. The political talks between them were arranged in 1979 after the Chinese dropped their condition that Soviet forces withdraw from Mongolia and those parts of Soviet territory that the Chinese claim. After three months of talks, all negotiations were dropped following the invasion of Afghanistan.

For the past year, the Kremlin has been pressing for their resumption with a series of overtures designed to take advantage of the Sino-American rift over President Reagan's policy toward Taiwan.

The souring of Sino-American relations has prompted speculation that China play its "Russian card," and Brezhnev today underscored Soviet readiness to play along.

In a related development today, the government news agency Tass distributed the text of a Soviet-Indian declaration signed by Brezhnev and Indian Prime Minister Indira Gandhi, who ended a six-day official visit here today.

In what was seen by observers here as an indication that Moscow was moving closer to India's position on Afghanistan, both sides "reaffirmed their conviction that the problems of the region demand peaceful political solutions paying full respect to the independence, sovereignty, territorial integrity and nonaligned status of the countries."

Diplomatic analysts here cautioned, however, that it remains to be seen whether Moscow intends to follow up with any concrete steps in Afghanistan, where there are about 100,000 Soviet troops propping up a pro-Soviet government.