The confrontation between the United States and Libya reaches beyond the Gulf of Sidra, Sudan, and Egypt to the heart of US policy in the Arab world - Saudi Arabia. Libya's threatened invasion of Sudan and Muammar Qaddafi's accompanying rhetoric is another round in the war between the widely divergent Islamic foreign policies of the quixotic Qaddafi and the House of Saud. With Saudi Arabia seeking security through Islamic solidarity and Libya using religion to foment revolution, the ongoing conflict has finally pulled the US into the vortex of the political and ideological struggle between the Islamic fundamentalists.
As if to prove the value of the US-Saudi alliance, strained by the Israeli invasion of Lebanon, the US has flexed its military muscle to quash the pan-Arab ambitions of the House of Saud's dreaded adversary. But US problems in the Middle East may not be helped by temporarily neutralizing Libya, as Saudi Arabia must increase pressure for vindication for its Muslim brothers and the recovery of Jerusalem in order to protect its shaky position in the Arab world.
The rise of Islamic politics has resulted from the vacuum in the traditional power centers in Arab politics following Camp David. With Egypt isolated by its treaty with Israel, Iraq bogged down in an inconclusive war with Iran, and Syria increasingly impotent, the struggle for leadership of the Arab world fell to the Islamic fundamentalists, Saudi Arabia and Libya.
It was Saudi Arabia's former king, Faisal, who conceived an alternative to total dependence on the superpowers for security and protection of its wealth. By combining its wealth and its spiritual legacy as the guardian of Mecca, Saudi Arabia could claim leadership of the Islamic world and then mold the Muslim states into a viable political bloc in the world's power structure. This policy, dubbed ''petro-Islam'' by skeptical observers, lay semidormant until Camp David, when it was resurrected.
Libya's Muammar Qaddafi, playing his own game with Islam, held a dangerous trump card against the Saudis. His cry of ''Islamic socialism'' combined the appeal of Islamic solidarity with the philosophy that the wealth of the oil states belongs to all Arabs. It was a message that caused Saudi Arabia and the oil-rich sheikhdoms along the Gulf to shudder.
But then came the oil glut and Lebanon. Qaddafi, once regarded as the most generous paymaster of instability in the Middle East, was seemingly defanged by Libya's financial problems. Shrinking oil markets cut Libya's petroleum exports from a high of $25 billion in 1980 to an estimated $8 billion in 1982.
In addition to the problem of meeting his bills, Qaddafi encountered a string of diplomatic disasters. He lost his foothold in Chad to the Saudi-backed Habre regime, failed to become chairman of the Organization of African Unity because of his inability to summon a quorum, and, finally, pulled his delegation out of last summer's meeting of the Organization of Islamic Conferences in a dispute with host country Niger.
But of all of Qaddafi's setbacks, nothing damaged his reputation with Muslims as much as his lack of posturing on behalf of the Palestinians during the siege of Beirut. As the Saudis called in their debts for past monetary gifts and publicly upbraided the US for its failure to control Israel, Qaddafi could offer nothing but the suggestion that Yasser Arafat commit suicide to preserve Arab honor.
This left Saudi Arabia, a country with 6 million people and no military power , as the major power broker of Arab politics. It was a tribute to the ingenuity and execution of petro-Islam. It may also have spelled the end of US illusions about its cozy relationship with the House of Saud.
Saud al-Faisal, the foreign minister, has consistently said that the greatest threat to the Arab world comes not only from the Soviet Union but from both of the superpowers. Although his statements receive little comment by Western political observers, they reflect a growing government policy. In remarks to a meeting of Islamic foreign ministers in Niamey in August, Prince Saud said: ''Each superpower formulates its policies according to its own interests and goals. The Soviet Union, which supports the Palestinian cause, has occupied the independent state of Afghanistan, while the US, which deplores the occupation of Afghanistan, has supported the Israeli occupation of Palestine. It is better for the Islamic nation to devise its own independent stand and not to rely on any foreign power.''
Saudi Arabia through economic and political pressure has become a major spoiler of recent US peace initiatives in the Middle East, because certain key conditions have not been met. Among these are the recognition of some form of Palestinian autonomy and Israeli withdrawal not only from Lebanon but from all of the occupied territories. Above all, the Saudis, as leader of the Muslim world, insist on the return of Jerusalem, for Jerusalem is the ultimate symbol of the Muslims' own diaspora.
But Saudi Arabia's position as the major spokesman and policymaker for the Arabs began to falter when it failed to stabilize oil pricing within OPEC. Sensing that Saudi Arabia was losing its grip on the underpinnings of petro-Islam, almost unlimited money, Qaddafi suddenly surfaced once again to champion the Arab cause. In the convoluted politics of the Arab world, the US must check Qaddafi's move into Sudan, thereby shoring up Saudi influence in the hope that the reluctant Saudis will then support both the Reagan peace initiative and the physical reconstruction of Lebanon.
By some miracle, this scenario might succeed. But realistically Saudi Arabia cannot afford to appear such a puppet of the US. The House of Saud has to continue to be an outspoken supporter of Palestinian rights and a forceful critic of Israel to protect its position both within the Arab world and with the Arab oil producers within OPEC. It cannot do otherwise because Muammar Qaddafi and his Islamic socialism lurk behind its throne.