The Greek government has abruptly called off a scheduled visit to the United States by a senior Cabinet minister in what diplomatic sources described yesterday as a sign of irritation over a "U.S. tilt toward Turkey."

There was no official explanation for the cancellation of the visit by Culture Minister Dimitri Nianias, who was to have arrived yesterday. A series of functions involving ranking U.S. political figures and educators had been scheduled, including the opening of an exhibition of ancient Cycladic sculpture at the National Gallery of Art next week.

Diplomatic sources said privately, however, that the government of Prime Minister Constantine Karamanlis was annoyed by what Greeks view as Washington's effort to molify Turkey to secure continued operation of U.S. intelligence monitoring facilities on Turkish soil.

Since the closing of U.S. intellingence gathering facilities in Iran following the shah's ouster, the value of similar American facilities in Turkey has increased sharply, especially because of verification problems connected with the new Soviet-American strategic arms limitation agreement.

Opponents of the SALT II accord have argued that the closing of the installations in Iran had seriously damaged the administration's ability to check up on Soviet compliance. Should the Turks close the U.S. installations on their soil, it would make the administration's position on verification even more uncomfortable.

The Turks have linked the future of the American installations to increased U.S. economic and military aid. The facilities which monitor Soviet missile tests and communications were shut down by Ankara in 1975 in retaliation for the congressional arms embargo on Turkey after the 1974 Turkish invasion of Cyprus. They were reopened last year after the embargo was lifted.

According to Greek sources, Athens sees Washington now as having virtually abandoned the Cypruss problem. A meeting between Turkish Cypriot leader Rauf Denktash and Prsesident Spyros Kyprianou is scheduled for next week, but these sources expect few positive results now that the Turks feel no U.S. pressure.

Moreover, the Turkish government is now blocking Greece's efforts to reenter NATO by raising the question of military responsibility for airspace over the Aegean Sea. Greece left the military arm of NATO in 1974 in anger over Cyprus. Turkey, like each other member of NATO, has veto power over Greece's re-entry.

While all other members of the alliance favor Greece's re-entry, the Turks are now insisting that their military forces be given responsibility for airspace extending 30 miles beyond Turkey's Aegean coastline. That would include the airspace over such Greek islands as Rhodes, Lesbos and Chios.

Greek sources said the Turkish request is "outrageous" and leaves hardly any room for compromise in the apparent impasse. They see little likelihood that the United States would press Ankara to abandon it during the current round of U.S. Turkish talks for the extension of the bases agreement, which expires in October.

Underlying Turkey's request is a Greek-Turkish dispute over the continental shelf in the eastern Aegean. The 1922 Laussance treaty gave Greece control of the area.

The cancellation of Nianias' visit at the last moment also reflects apparent frustrations in Athens over the fact that the problem of American intelligence-gathering installations in Turkey has strengthened theposition of Ankara both within NATO and in Washington.

Instead of the culture minister, Athens is sending an undersecretary in the Foreign Affairs Ministry, Andreas Andrianopoulos.