CONDITIONS may be ripe to break the political deadlock in Cyprus. Ending the tension between Greeks and Turks in the island nation - which in turn has inflamed ancient friction between Greece and Turkey - would better the lives of all Cypriots, and also would enhance stability on Europe's (and NATO's) southeastern flank.During his visits to Athens and Ankara last week, President Bush extended United States support to the efforts to solve the Cyprus crisis, offering to be a "catalyst" in the process. It's unlikely that he leaped recklessly into a dispute that has defied nearly three decades of United Nations mediation. Ever since the former British colony gained independence in 1960, bad blood has infused politics between the majority Greek Cypriots and the Turkish Cypriots, who comprise 18 percent of Cyprus's population. Since 1964 a UN peacekeeping force has maintained a "green line" between the communities. Despite the UN presence, pro-Greece extremists overthrew the government in 1974, and shortly thereafter Turkish army forces landed to secure the northern two-fifths of the island inhabited by Turkish Cypriots. To day some 30,000 Turkish troops are stationed on Cyprus. Among the promising developments is new, more moderate leadership in Greece and Turkey. In both countries, politicians are somewhat less inclined than before to wave the Cyprus flag for domestic political reasons. Also, in both countries leaders are eager to bolster relations with Europe and the United States. Turkey, in particular, wants to capitalize on its heightened prestige coming out of the Gulf war and to strengthen its application for admission to the European Community. Both Ankara and Athens ar e likely to see foreign-policy objectives frustrated while they appear to be patrons of unrest in Cyprus. While leaving administration of the negotiations in Cyprus in the hands of the UN, the United States should, as President Bush implied, use its influence with Turkey and Greece to call for moderation and good faith in their dealings over Cyprus. For their part, Turkey and Greece should urge upon their Cyprus compatriots flexibility in devising new territorial and political arrangements there.