The beginning of the third Kennedy presidential campaign in a generation is being handled with careful attention in Moscow, puzzlement in Peking and a mixture of fascination and wariness in other world capitals, Washington Post foreign correspondents report.

Foreign reactions to the declared candidacy of Sen. Edward M. Kennedy vary widely , but seem to contain common threads of uncertainty about his true position on a number of key issues and a certain amount of nostalgia for what -- in retrospect -- seem to be the simpler times of the 1961-63 presidency of John F. Kennedy.

That nostalgia is only part of the foreign fascination with Teddy Kennedy, the survey of Post correspondents suggests.

Equally important has been the wide exposure of Kennedy to foreign leaders and public opinion through the intensive working trips he has undertaken to virtually every major world capital in recent years. This has been reinforced in the last month by a busy schedule of interviews Kennedy has granted foreign media.

The official Soviet media had paid more positive and careful attention to Kennedy over the years than to any other American political figure, Kevin Klose reported from Moscow. He received extensive coverage during 1974 and 1978 visits, which included lengthy conferences with Soviet leader Leonid Brezhnev, who is said to have a special regard for Kennedy.

The view that emerges in conversions with Communist Party members bureaucrats and others is that Edward Kennedy may be the inheritor of John Kennedy's advocacy of confidence-building measures like the 1963 treaty banning nuclear tests in the atmosphere, Klose notes. Edward Kennedy's support for strategic arms control, detente and other bilaterial accords are frequently reported in the Soviet media, although not in detail.

It is Kennedy's support for the SALT II arms treaty that is most troubling for the Chinese, who are at the same time pleased with his early support for normalization of U.S.-China relations, Jay Mathews cabled from Peking.

Peking's official attitude toward any U.S. politican depends almost entirely on that politican's public position toward the Soviet Union, Mathews noted. One diplomat jokingly said that the Chinese seemed to feel Kennedy "tends to be soft on communism" because of his support for SALT and detente.

Kennedy visited China during the Christmas holidays in 1977 and told Chinese Vice Premier Deng Xiaoping that he supported a strong U.S. defense policy. He also visited schools, private homes and a prison, and urged the chinese to loosen their restrictions on emigration of people with families in the United States.

The Chinese have liberalized emigration since Kennedy's visit. Kennedy's staff adviser for foreign policy, Jan Kalicki, visited Peking in August to maintain the Kennedy contact.

In Paris, Bonn and London the Kennedy candidacy has provoked no enthusiasm from the ruling governments or media, but is attracting wide interest.

The French media are treating Kennedy like a star, and a winner, Ronald Koven reported from Paris. French magazines are devoting covers to "The Kennedy Myth" and he is being featured in lengthy television interviews.

Although the Kennedy name has a special ring in West Germany because of JFK's "ich bin ein Berliner" ("I am a Berliner") declaration, it is not at all clear that Sen. Kennedy can benefit from that emotional symbolism, according to Michael Getler in Bonn. Bonn's leadership is showing no great enthusiasm for a candidate who, the West Germans fear, may emphasize social programs at the expense of defense spending.

Kennedy's reputation as a big government spender is also out of official fashion in Margaret Thatcher's Britain, Leonard Downie, Jr. reported. His Irish Catholic heritage also bothers Britons and the unease is intensified by his support for the principle of the unification of Ireland and British-ruled Northern Ireland.

Even in the Middle East, where Kennedy's strongly pro-Israel stands might be expected to produce a clear profile of reaction, he is viewed with mixed expectations and no small measure of wariness.

William Claiborne in Jerusaleum said that Israeli officials are treating the upcoming Democratic primary with extreme care in light of Israel's $3.4 billion aid request now before the Carter administration.

Conservative advisers close to Prime Minister Menachem Begin have not been totally reassured by Kennedy's declarations on the Middle East, which included a new message to Begin last week reemphasizing Kennedy's opposition to any U.S. negotiations with the Palestine Liberation Organization and his support for an undivided Jerusaleum.

But Begin's advisers do appear to be encouraged by their perception of the Kennedys as a tribe of traditional internationalists who would reverse what is often seen in Israel as America's retreat from commitments to a global role. Moreover, they like the fact that Kennedy is a Democratic Party regular and would work with a party establishment that has many friends of Israel in its top ranks.