Turkish and Greek Cypriots have agreed to resume negotiations toward reunification of the war-torn island in what U.N. Secretary General Kurt Waldheim today called a "breakthrough" that "for the first time provides a chance of solving the Cyprus problem."

Turkish Cypriot leaders Rauf Denktash and Greek Cypriot President Makarios, who met yesterday for four hours with Waldheim, announced today that talks between the two sides, which were broken off a year ago, would resume next month in Vienna.

Although both sides reportedly made major concessions in their previous demands on territory and government structure, all the participants stressed today that the new departure represents only the start of a long negotiating process that Denktash said, "might produce a solution in a year or 18 months."

Denktash said today that the new negotiations will be based on a plan for a federal, two-zone republic for Greek and Turkish Cypriots on this divided island.

U.S. concern for an early solution in Cyprus was obviously a major factor in the "breakthrough." In separate press conferences, a future U.S. role in the bargaining was referred to enthusiastically by Makarios, suspiciously by Denktash. Clark Clifford starts a mission here next week to find ways in which the Carter administration can be "helpful in finding an accommodation."

The new negotiating formula accepts Turkish Cypriot control over nearly a third of Cyprus in an area of the island adjacent to Turkey where Turkish Cypriots will enjoy a real measure of autonomy and feel secure from the Greek Cypriot majority.

In return, Greek Cypriots are promised some Turkish withdrawal from the present cease-fire lines and the restoration of some Greek Cypriot refugees' land. The Turkish Cypriot side also agreed to recognize "in principle" the right of settlement and property for Greek and Turkish Cypriots throughout the island.

The negotiating framework, designed to eliminate the conflicts that have deadlocked the talks, is a written document that the two Cypriot leaders worked out "word by word," Waldheim said. The guidelines are confidential, apparently as part of an attempt to retain a measure of secret diplomacy.

The document states that Cyprus will be an "independent, nonaligned, bicommunal, federal republic," Denktash said, reading from the official text. Earlier Makarios had used similar words, but added that Cyprus would remain a single state.

Widely acknowledged privately on both sides as the most realistic approach to a settlement, this trade-off - an autonomous region for Turkish Cypriots and some central authority that may grow in time for the Greek Cypriots - has only now been accepted publicly by the two leaders.

Makarios, aided by semantics, seems to have made concessions on several points that he originally contested.

The biggest change in bargaining positions was to base territorial claims not on the ratio of land to population that Makarios insisted would require the Turkish Cypriots to reduce their occupation from the present 38 per cent to 20 per cent but on "land ownership and land productivity and the economic needs of the two areas." The new formula appears flexible enough to allow the two sides to compromise at around 30 per cent for the Turkish Cypriots, the Greek Cypriots hope.

Makarios told a large press conference in his archbishop's palace that the new state would be "bicommunal," but diplomats interpreted this phrase as cosmetics for the current "bizonal" situation in which the separation of population into two homogencous zones is almost complete.

Denktash held his press conference in the unused basement night club of a hotel only a few hundred yards away, across the U.N. enforced ceasefire line dividing this capital. He announced that the "right of settlement and property" could only be implemented with due regard for Turkish Cypriot security and the need to preserve a majority in their own area.

Speaking of a withdrawal, however, Denktash added that the new line to be negotiated would "solve many problems" for the estimated 125,000 Greek Cypriot refugees who outnumber the 110,000 Turkish Cypriots. Diplomats suggested that Makarios hopes to be able to resettle at least half his refugees in regions reopened to Greek Cypriot control, perhaps around Famagusta, and through an agreement that would allow some Greek Cypriots to return north.

Makarios refused to be drawn out on whether the projected federal government would be "weak or strong," but Denktash made its limitations clear. The army, Denktash said, should have a central command, with Greek and Turkish Cypriot wings in their respective areas only for a long time.

Denktash said he had asked for an end to Greek Cypriot "popaganda and economic warfare" against the Turkish Cypriots, but Makarios, who announced his new position to the Greek Cypriot parties today, has refused to commit himself publicly.

Denktash flatly ruled out the return of any refugees until a settlehent was reached. He said many Greek Cypriots would prefer not to return once they realized they would have to live under Turkish Cypriot authority.

The first hints of reconciliation may have surfaced in the enthusiasm with which Turkish and Turkish Cypriot journalists today sought to be photographed with a smiling Archbishop Makarios.

Greek Cypriots, crossing to the Turkish-held area for the first time since the Turkish invasion in 1974, were much more agressive in questioning Denktash, but were told "present generations must accept sacsternly that they must realize that the rifices to avoid a repetition of our past troubles."

U.S. interest was welcomed by Makarios, who said he thought the United States might "help bridge the remaining gaps" between the two sides views on territory and constitutional change.

In contrast, Denktash said he feared a one-sided U.S. interest influenced by Carter's campaign debt to the "Greek Lobby." He admitted, however, that his own diplomatic activity was spurred partly by the imminent arrival of Clifford, whom he welcomed as a "factfinder not a recipe maker."