In the developing and sensitive relationship between the United States and Saudi Arabia, the government in each country has to play to two conflicting constituencies.
For the US, those two constituencies are the moderate Arab world on the one hand and, on the other, Israel and the powerful pro-Israel lobby in American domestic politics.
The US found itself once again torn between these two demands as the United Nations Security Council went into session Jan. 5 to consider what to do about Israel's refusal to rescind its legislation effectively annexing the Israeli-occupied Syrian Golan Heights.
For Saudi Arabia, the conflict arises when it tries to woo US official and public opinion and, at the same time, seeks to bring hard-line Arab governments into a united front behind Saudi policy - or on an agreed negotiating position in the search for an overall Arab-Israeli settlement.
The Saudi dilemma has been spotlighted this week by the zigzag that Saudi officialdom has taken in the wake of an interview given by Saudi Foreign Minister Prince Saud, clearly directed at reassuring the Saudis' American constituency.
Saudi backing and filling has two immediate consequences in Israel. First, it gives the Israeli government grounds for saying that there is so much equivocation in the Saudi position that Israelis remain unconvinced that the ultimate Saudi aim is no longer the destruction of the state of Israel. It also provides an opening for Israelis to try to wreck the US-Saudi relationship, seen by Prime Minister Menachem Begin's government as the single greatest threat developing in the Arab world against Israel.
Prince Saud was quoted in the New York Times Jan. 3 as having spelled out for the first time Saudi Arabia's terms for the acceptance of Israel. The prince obviously had his eye on the US as he spoke - and on the need to persuade the Reagan administration to be as pro-Arab as possible in this week's Security Council debate on Israeli action over the Golan Heights.
The relevant paragraph in the report on the interview read in part:
''The Saudi foreign minister said . . . that in return for Israeli recognition of Palestinian rights and the return of occupied Arab lands, his government was prepared to 'accept it' - referring to Israel.''
Twenty-four hours after publication of the interview, the state-run radio in the Saudi capital, Riyadh, was quoting a Saudi Foreign Ministry spokesman as saying:
''There is absolutely no truth in what has been attributed to . . . Prince Saud about the kingdom's recognition of Israel. What . . . Prince Saud said with regard to recognition was in essence a reference to the requirement that Israel recognize the rights of the Palestinian people to return to their land, to self-determination, and to the establishment of their independent state with Jerusalem as its capital.''
The spokesman was quoted further as saying that ''peace can prevail in the region'' once these conditions were met.
But these conditions - which Saudi partisans might argue is an extreme opening position for eventual negotiation - have repeatedly been rejected out of hand by the Begin government in Israel.
In Israel, there was no offical comment on the Saudi zigzag. But privately Israeli officials said statement and then disavowal were part of an established Saudi pattern.
Whether or not the broadcast over Riyadh radio was in fact disavowal, the Saudi Foreign Ministry spokesman was clearly addressing his government's Arab (as opposed to US) constituency.
The Saudi government cannot afford to let itself appear in the Arab world too ''soft'' toward either Israel or the US at the very moment when Israel has effectively annexed Golan; the US may be preparing to veto or block any UN Security Council move to impose punitive sanctions on Israel; and bridges are being mended in a surprising effort to restore a united Arab front of moderates and hard-liners.
(At time of writing, Arab League and Saudi leaders were meeting in Riyadh to discuss the possibility of an Arab summit conference to discuss the Israeli annexation of the Golan Heights, according to the official Saudi press agency.)
In late December, there was reconciliation between hard-line Syria and Saudi Arabia, with Syrian President Hafez Assad visiting Riyadh less than a month after he had offended the Saudis by helping torpedo their Middle East peace plan at the Arab summit in Morocco.
With Saudi blessing, Mr. Assad is preparing to visit the hard-line states of Algeria and Libya to try to bring them into a broader unified Arab fold. At the same time, the Saudis have encouraged Mr. Assad to ensure that King Hussein of Jordan, a moderate rather than a hard-liner, is not alienated by being overlooked. And in another conciliatory gesture, Saudi Interior Minister Prince Nayif has recently visited hard-line Iraq.
This is the context within which Riyadh radio's apparent disclaimer about the Prince Saud interview should be seen.