From one end of the Arab world to the other, the United States is now being offered an unprecedented opportunity to exert its influence.
At first hesitant to react to the Israeli invasion of Lebanon, Egypt has added its urgent voice to that of Saudi Arabia in calling on the US to recognize the need for Palestinian self-determination and to act on it.
These two Arab countries, one the most powerful and the other the wealthiest, are far apart on many issues. But on the Palestinian question they seem to have drawn closer in recent weeks. In effect, the two Arab nations are saying that if the US fails to move toward a comprehensive peace in the region, it could end up with an Israeli occupation of southern Lebanon and a Palestine Liberation Organization (PLO) more radical than that which now exists.
America's major Arab ally, Egypt, is pressing for political concessions from the US on the Palestinian issue at a time when it appears from here that the PLO's military fortunes are at a low point. According to Egypt's ambassador to Washington, Asraf Ghorbal, PLO chairman Yasser Arafat's statement of July 25 to US congressmen, which accepted United Nations resolutions relating to the Palestinians, is a step in the right direction and ought to be encouraged. The same message is expected to come from the Egyptian foreign minister, Kamal Hassan Ali, when he visits here later this week and meets with Secretary of State George P. Shultz.
But the US reacted with caution to the Arafat statement. Reagan administration spokesmen moved quickly to assert that it does not meet American conditions for recognition of the PLO or negotiations with that organization.
US officials said that Arafat's statement to congressmen visiting Beirut was vague and misleading and did not explicitly recognize Israel's right to exist. The officials also seem concerned that if they appear to be moving in the direction of direct talks with the PLO, it might cause Israel to preempt the PLO by moving on West Beirut.
There is nothing new in the Egyptian line that the US ought to accept Palestinian self-determination and open a ''dialogue'' with the PLO. The late President Anwar Sadat made a number of statements to this effect. But the Egyptians are now speaking with a sense of urgency that seemed to be absent at the outset of the current Lebanon crisis.
The Egyptians are not threatening to withdraw from the US-supported, but now stalemated, Camp David peace process they undertook in 1978 with Israel. But they want to reinvigorate the Egyptian-Israeli talks with a impetus toward solving the Palestinian question. Their actions seem to indicate that if there is no progress within the Camp David process, then they are likely to drift away from further accommodation with Israel. Partly because of the Iran-Iraq war, meanwhile, the Egyptians are drawing closer to Arab nations that opposed Camp David.
Earlier this month, Iraq invited Egypt to a meeting of leaders of nonaligned nations and Egyptian President Hosni Mubarak accepted. Egypt also began calling for a collective Arab position on the Lebanon crisis. As many observers have noted, the Arab world is possibly more divided now than it has ever been. But on the Palestinian issue, many Arab nations seem to be stressing a common theme.
One reason for this may be pressure on the Arab leaders from their own home constituencies. The rapprochement with Israel has come under increasing attack within Egypt from a variety of critics. Put in its crudest terms, the critics are charging that President Sadat ''sold out'' Egyptian interests to both the Americans and Israelis.
In a breakfast meeting with reporters, Egyptian Ambassador Ashraf Ghorbal said that the PLO has been ''inching forward'' toward recognition of Israel and that the US ought to acknowledge and encourage this.
''Yasser Arafat should be encouraged more,'' said Mr. Ghorbal. ''He is going to move from a humiliating military defeat to a recognition of the state of Israel. . . . Help the man to cross the road. . . . If you tell him to 'get on your knees and crawl across,' it's not helping him to cross that border. . . .''
Ghorbal argued that if the US fails to tie a solution of the Palestinian issue to a solution of the Lebanon crisis, then he could visualize a ''repeat performance,'' where Israel moves next to take over the occupied West Bank and Gaza through a kind of de facto annexation.
''If you let Israel annex the West Bank, or you acquiesce in it, you can forget all of us.''
''Yasser Arafat, very frankly, is the most reasonable of the lot, and his group, Fatah, has been the most reasonable,'' said Ghorbal.