Cairo — Publicly, Egypt has asked the United States to open contacts with a ''moderate'' Yasser Arafat in the wake of his reconciliation visit to Cairo. And in the best of all possible worlds, Egypt would, indeed, like precisely that.
Yet privately, the Egyptians are deeply skeptical of early prospects for concil-liation by either the US or Arafat's Palestine Liberation Organization.
Cairo's main aim at present is to preserve what it sees as ''momentum for moderation'' in the Mideast created by Arafat's controversial talks with Egyptian President Hosni Mubarak. It also wants to stem the rival ambitions of parties like Syria, Iran, and the ever more assertive terror groups striking in the name of Shiite Islam.
The public call for a US overture to Arafat is part of this effort to ''keep up the momentum'' for moderation. Further such moves are likely, especially in light of Egypt's assumption of a seat on the United Nations Security Council.
The Americans, Cairo officials are assuming meanwhile, will be leery of any major Mideast negotiating shift in a US presidential election year.
And Arafat, whose primary preoccupation with PLO unity has long militated against any definitive shift from military to political tactics, has still not visibly indicated he is ready to make such a move.
The Egyptians do think the PLO chief is more likely than in the past to opt for olive branch over gun. But they are concerned that Arafat might backtrack from the negotiating route due to a combination of hard-line pressure from within Palestinian ranks and a lack of visible incentive from the Americans - much less, Israel.
''I believe nothing will happen until after (the US elections) next November, '' a Cairo source says. ''What is important at present is not a final negotiated solution, but to fill the gap until then'' with visible efforts to keep negotiation prospects alive. Private remarks from officials suggest three related reasons Egypt sees this as important:
* To keep ''world opinion'' focused on the need for a negotiated resolution of the Palestinian ques-tion.
* To ''contain extremists'' in the region who oppose any such resolution and will be quick to seize on indications that such an option is impractical.
* To ''give hope to the moderates'' in the region.
So far, the Egyptians are basically pleased with Arafat's visit to Cairo and the US response to it. The US, despite sharp criticism from Israel, publicly welcomed Arafat's talks with Mr. Mubarak.
But Egypt's fear is that the US welcome for the Arafat move will erode with time and domestic political dynamics; and that the PLO chief, in the words of a Cairo source, will demonstrate an ''incapacity to move'' decisively toward a negotiated Mideast settlement.
Despite suggestions in the Western news media that Mr. Mubarak, in his talks with Arafat, revived past Egyptian calls for a Palestinian ''government-in-exile ,'' the advice offered seems in fact to have been less specific.
The view here is that the initial rationale for recommending a Palestinian government-in-exile - that it might win Arafat widened international acceptance - no longer holds. If such a move were made now, the Egyptians feel, it might well have the opposite effect. Rival Mideast parties like Syria and Libya - not to mention the US - would likely withhold support.
''What is important is that something, anything, be done by Arafat to keep up the momentum,'' maintains an official privately. This ''something,'' it is suggested here, could involve renewed talks between Arafat and Jordan's King Hussein. Or it could entail reviving last year's joint UN initiative by Egypt and France to in effect trade more energetic Security Council endorsement of Arafat's political goals in exchange for a muting of PLO emphasis on its ''armed struggle'' against Israel.
''The windfall of the Arafat-Mubarak meeting,'' says another official, ''is that it suddenly placed the Palestinian problem in the international limelight again. . . .
''But what is important is the follow-up to that meeting. The importance of the meeting itself should not be overemphasized. It is only a first step.''