President Spyros Kyprianou of Cyprus flew to Athens this week seeking Greek support in his dispute with the United Nations over its latest proposal to reunify the divided island.

At the heart of the quarrel is Kyprianou's opposition to the draft document presented by U.N. Secretary General Javier Perez de Cuellar, calling for a federated Greek and Turkish Cypriot state with a presidential system of government and a two-chamber legislature, on the grounds that it is too favorable to Turkish Cypriot leader Rauf Denktash.

The dispute has embarrassed the Greek Cypriot leader's government at home and generated resistance among Greek Cypriot opposition leaders to anticipated calls from Athens for a united front.

Turkey invaded Cyprus in 1974 after an abortive coup backed by the junta then in power in Greece. Turkish troops underpin Denktash's control of the northern part of the strategically located island. His self-declared Turkish Republic of Northern Cyprus comprises about 37 percent of the island's area and Turkish Cypriots make up about 18 percent of its population.

Kyprianou has led the Greek Cypriot state in the south since 1977, and has rejected a number of settlement plans because he considers them too generous to the Turkish Cypriots.

Perez de Cuellar, whose peace intiative began in 1984, presented his third and latest plan in March. A letter from Kyprianou to the U.N. chief detailing his problems with the new draft noted provisions for weighted voting and the veto power that would be given to the Turkish vice president in the federated state. He also was critical of the lack of provisions for withdrawal of Turkish troops from the island, of international guarantees for the accord and of arrangments to ensure that the two communities could work, move and live freely throughout the island.

Perez de Cuellar reinforced Kyprianou's opposition to the latest plan earlier this month by describing as "not viable" -- because of Denktash's objections -- the president's subsequent alternative suggestions for an international conference under U.N. auspices or top-level talks between Greek and Turkish Cypriot leaders.

Perez de Cuellar also warned of the "dangers inherent" in the continuing deadlock over Cyprus, where conflicting communal aspirations have fostered longstanding tensions both on the island and between Greece and Turkey, two key NATO members on the southeastern flank of the alliance. A U.N. spokesman pointedly said the eight countries contributing to the 2,328-man U.N. buffer force between Greek and Turkish Cypriot lines on the island had been doing so since 1967, adding that "there should be no tendency to take its existence for granted."

In an apparent bid to encourage an impression of movement in the negotiating process, a low-level Soviet Foreign Ministry delegation suddenly arrived in Cyprus earlier this month at Kyprianou's invitation to push its longstanding plan for an international conference just like the one suggested by the Greek Cypriot leader.

While the Soviets maintained that they still backed the U.N. "good offices" mission here, their plan called for the removal of not only the estimated 18,000 mainland Turkish occupation troops from the north, but also two so-called "sovereign" British bases ceded when the former British colony became independent in 1960.

Removal of the British bases, which has long been a Soviet policy objective, did not figure in the world body's negotiating brief.

Although Greek Cypriot government spokesmen publicly expressed their "sorrow" about differences with Perez de Cuellar, they also have hinted that the U.S. and British governments intervened at the last minute to influence the secretary general's report encompassing his latest proposals, which was published on June 11. The U.S. Embassy denied the charge.

In an interview, Greek Cypriot Foreign Minister George Iacovou regretted what he called the "poor advice" the U.N. secretary general allegedly had received. He maintained that a "friendly source," whom he declined to name, had provided the draft of the U.N. report showing changes "in the space of a few hours" before it was published.

Denktash and some Greek Cypriot opposition leaders say they are convinced that no negotiated settlement for Cyprus is possible until Kyprianou leaves office.

That prospect is a source of anxiety within NATO, which fears the destabilizing effects in the region of the island's continued partition.

Kyprianou, for his part, shows no desire to quit even after his current term expires in 1988. His Democratic Party last year scored impressive gains in legislative elections by taking a hard line on the negotiations.

Glafcos Clerides, veteran leader of the right-wing Democratic Rally Party, has defined Cyprus as suffering from two, irrational "anguishes": the Greek Cypriot conviction that Turkey intends to take over the whole island and the Turkish Cypriot fear that Greek Cypriots still want "enosis," or union with Greece.

"Attach a tugboat and tow it into the Atlantic," he said in an interview, "and the problem of Cyprus is solved in 24 hours." But no such end to the long stalemate -- or ethnic tensions -- is in sight, according to diplomats and observers here.

Now, apparently emboldened by the setback to Perez de Cuellar, Denktash has invited Turkish Prime Minister Turgut Ozal for an official visit beginning July 2, the first such high-ranking sojourn since the north was proclaimed an independent breakaway state in 1983.

The prospect of Ozal's presence has set off shock waves among Greek Cypriots with officials worried that it is a prelude for other countries to join Turkey in recognizing the Denktash regime.

Vassos Lyssarides, the Greek Cypriot socialist leader, has vowed to hold a massive protest rally.

Even without the Ozal visit, July is always a potentially explosive time as Greek Cypriots mark the anniversary of Turkey's invasion with demonstrations and rallies.