NINE months after replacing Margaret Thatcher as prime minister, John Major is generating favorable comparisons with the "Iron Lady" as an effective operator on the world stage.His advisers say public appreciation of Mr. Major's diplomatic skills is likely to help him in his coming bid to keep the ruling Conservatives in power for another five years. A two-week burst of international diplomacy by Major, ending last weekend, has already helped to propel the Conservatives into a narrow-opinion poll lead over the Labour Party after months of trailing behind the opposition. Major's spate of globe-trotting, on the eve of Britain's annual political party conference season, took him first to talks with President Bush at Kennebunkport, Maine, where he drew presidential praise for his "penetrating analysis" of the failed Kremlin coup and its implications. Mr. Bush later spoke of an "extraordinarily special relationship" forged between Washington and London since Major took office last December. The prime minister then flew to Moscow and, as current chairman of the Group of Seven industrialized nations, outlined Western aid plans to President Mikhail Gorbachev and the Russian president, Boris Yeltsin. He was the first Western leader to visit Moscow after the coup. From there Major traveled to Beijing where he publicly - and against the advice of his own officials - lectured his hard-line Chinese hosts on their poor human rights record. "It is the unremitting, unrelenting continuance of pressure that often yields results," Major told a press conference. Soon after the prime minister left Beijing, Liu Haijing, a Hong Kong businessman accused of helping Chinese dissidents, was released from custody. In Beijing, Major also obtained China's signature on an agreement with Britain for work to begin on a new airport for Hong Kong. Later, in Hong Kong, Major set out to reassure the territory's people that after 1997, when the mainland Chinese take over, Britain would insist on the capitalist system continuing there for at least half a century. Within three days of his return to Britain, a trio of opinion polls showed the Conservatives between two and four points ahead of Labour, with Major's own personal approval rating well ahead of that of Neil Kinnock, the opposition leader. The polls prompted speculation that Major might call a general election as early as November. Later in carefully phrased statements to the media, the prime minister tried to discourage that idea. Conservative Party officials, already preparing for the general election which Major must call some time before mid-1992, have begun weighing the likely impact of Major's diplomatic successes upon the British electorate. One official said: "We still have problems with the economy, but they are beginning to ease. John Major's success in the international arena is likely to boost his status and popularity, as it did with Margaret [Thatcher]." The precise extent to which international diplomacy can help a British prime minister in domestic politics is debatable. Professor Ivor Crewe, a leading opinion poll analyst, said any prime minister would need to build up a steady lead for his party of 6 to 8 points for several weeks before risking a general election. A Conservative member of Parliament commented that in a three-week election campaign, foreign affairs might dominate the early stages. But in the closing phase, "people would be more likely to dwell on such matters as rising unemployment and steep interest rates. I think John Major would be taking a mighty gamble if he thought his international reputation would see him through to victory." That estimate may underplay two important factors. Major, his close friends say, is keen to obtain a personal mandate from the electorate as soon as possible. He displaced Mrs. Thatcher as Conservative party leader in controversial circumstances. Major also is looking ahead to December when Britain at a European Community summit at Maastricht, Netherlands will be asked to give full backing to closer EC political and economic integration. At the Maastricht summit Major's hand would be enormously strengthened if he had won a general election the previous month.