There was never any doubt that Egyptians would honor President Sadat's wishes in confirming Hosni Mubarak as his successor. Tuesday's referendum was a formality -- a way of bringing ordinary Egyptians into the preordained succession process. And the burly former Air Force pilot will officially take office with his swearing in Oct. 14.
But if the new Egyptian president is to establish himself as a valid national leader, let alone a central figure on the broader. Middle East stage, he needs to chalk up early gains on at least three vital foreign policy fronts:
* He must ensure that nothing happens to give the Israelis any cause or pretext not to meet their obligation under the Camp David accord to withdraw from the last sliver of Egyptian territory in the Sinai by April 1982.
* He must secure from the Israelis, presumably with American help, a more meaningful commitment to "full autonomy" for the Palestinians on the West Bank than Israeli Prime Minister Menachem Begin was willing to give the late President Sadat.
* Yet, at the same time, he must try to reverse one of the most dangerous legacies left him by the late President Sadat -- Egypt's isolation from the rest of the Arab world. Central to this task is rapprochement with Saudi Arabia, whose role in the Middle East is increasingly crucial.
These three counts are interconnected. They may, in fact, prove mutually exclusive.
If Mr. Mubarak digs in his heels on the Palestinian issue, he risks alienating Mr. Begin and driving him to delay Israeli withdrawal from Sinai. Yet unless Mr. Bubarak gets concessions from Mr. Begin on the Palestine issue -- or can convince the Saudis that Egypt will not sell the Palestinians down the river -- there is little hope of Saudi Arabia's responding favorably to any other conciliatory gestures from him.
The Reagan administration has apparently been stirred by the events of the past week to recognize both the urgency of the Palestine issue and the fact that Mr. Mubarak has less freedom of movement on it than had Mr. Sadat. For one thing, Mr. Mubarak, as a freshman president, may not feel able to take the same risks that Mr. Sadat might have.
Hence, presumably, US Secretary of State Alexander M. Haig's public expression of hope at the weekend that Israel would go slow on expanding Jewish settlements on the West Bank -- an anathema to Palestinians and an embarrassment to the Egyptians.
And fitting into the same picture is the White House release of remarks by former Presidents Carter and Ford about the eventual need for the US to have discussions with the Palestine Liberation Organization in the search for a settlement of the Palestine issue.
All this is a far cry from the White House attitude during Mr. Begin's visit to Washington last month. If Mr. Begin is to be believed, President Reagan never once raised with him the question of Jewish settlements on the West Bank.
As for Egyptian-Saudi rapprochement, the uncertainties in the wake of hte Sadat assassination paradoxically reintroduce a flexibility that deep-rooted Arab hostility to Mr. Sadat had previously removed.
One can only assume that the Reagan administration, sensitive to this, is seizing whatever opportuinity it can its dealings with the Saudis to argue the benefits of a closer relationship with Egypt. This could well be one of the underlying, unspoken objectives of former President Nixon's journey to Saudi Arabia after the Sadat funeral.
But Washington's effectiveness in this direction is bound to be inhibited for the moment by the increasingly bitter fight within the US over the proposed sale of AWACS planes to the Saudi government.
This gives greater importance to current European initiatives in the direction of both Saudi Arabia and the Palestinians. French President Francois Mitterrand visited Saudi Arabia last month and conferred with both King Khalid and Crown Prince Fahd. British Foreign Secretary Lord Carrington is to visit Saudi Arabia later this month.
Lord Carrington, currently president of the European Community's Council of Ministers, has EC backing to try to get the Palestinians (or people who can influence them) to bite the bullet and publicly accept the possibility of an Israeli and Palestinian state existing side by side.
Saudi Arabia, with its funding of the Palestinians, does have influence with them. So it si worth noting that the current Saudi peace plan for the the Middle East -- endorsed with some reservations by President Mitterrand as a starting point for overall Mideast peace negotiations -- does recognize " the right of all states in the region to live in peace." (Most third parties accept this as Saudi recognition of Israel's right to exist.)
The Saudi plan announced by Crown Prince Fahd Aug. 7 and reaffirmed in the United Nations General Assembly last month by Saudi Foreign Minister Prince Saud , has gotten little attention in the US. But Israel is apparently aware of how Western, and particularly US, acceptance of the Saudi plan as a basis of negotiation could upset the aim of Mr. Begin and other Israeli hard-liners to eventually annex the West Bank.
Speaking in New York Oct. 5, Israeli Foreign Minister Yitzhak Shamir described the Saudi plan as "a prescription for the dismemberment of Israel, not for peace with Israel.