On his current visit to the Middle East, Alexander M. Haig Jr. is trying to give fresh impetus to the stalled Egyptian-Israeli talks on Palestinian autonomy.
But the American secretary of state is having to tread with great care.
Israel is very sensitive on the Palestinian issue and to pressure from its United States patron. Mr. Haig has to avoid giving Israel any pretext for reneging on its commitment to complete its withdrawal from Egyptian Sinai by April 25.
At the same time, he has to take account of the conflicting views of the Egyptians and the Israelis on two aspects of the Palestinian issue:
* Interpretation of the ''full autonomy'' for the Palestinians to which Camp David commits the signatories.
* The framework and timetable within which that autonomy shall be negotiated.
The Israelis insist on the narrowest possible interpretation of ''full autonomy.'' They are determined to block any path that might lead to Palestinian self-determination or statehood.
The Egyptians, on the other hand, want the broadest possible interpretation of ''full autonomy.'' They insist that the path must be kept open to Palestinian self-determination or statehood (and hence also to Egypt's eventual acceptance back into the Arab fold).
As for the timetable and framework for continuing discussions, the Israelis are set on keeping strictly to the letter of the Camp David formula. They are against broadening the forum for future negotiations.
If Palestinians are brought into the talks, the Israelis want only ''tame'' ones -- and certainly not the Palestine Liberation Organization (PLO). And they are utterly opposed to any alternative forum to Camp David, such as the on-again , off-again Saudi peace plan.
The Egyptians believe no progress can be made on Palestinian autonomy without the participation of truly representative Palestinians. (They do not specify the PLO.) They are not averse to a broader forum -- reportedly not even to the Saudi plan at the right moment. And they are ready to resist any pressure on Egypt in the coming weeks to make concessions toward the Israeli interpretation of ''full autonomy'' as a quid pro quo for securing Israeli withdrawal from Sinai as scheduled by April 25.
Hence, the Egyptians will be reassured by the way Mr. Haig's talks with President Mubarak went Jan. 13. The two men agreed there should be no deadline for the autonomy negotiations -- thereby precluding any deal at Egypt's expense by April 25. Mr. Haig said Mr. Mubarak had promised to cooperate in giving the talks fresh impetus and was willing to broaden them.
But all this is enough to set warning lights flashing -- if not alarm bells ringing - in Israel, where Mr. Haig was due Jan. 14.
Mr. Haig will be the first member of the Reagan administration to meet Israeli Prime Minister Menachem Begin since US-Israeli relations came under such strain last month with Israel's virtual annexation of the Syrian Golan Heights. On that particular issue, ruffled feathers may have been smoothed by:
1. The reported US assurance to Israel that the American veto will be used in the UN Security Council to prevent sanctions being imposed on Israel for its Golan action.
2. A ''friendly'' message -- to quote Israel radio -- from President Reagan to Mr. Begin telling the latter that their differences were ''a thing of the past.''
Whether this message has done anything to remove Israeli suspicions of the Reagan administration's long-term intentions in the Mideast is quite another matter. The developing US-Saudi relationship -- seen as at Israel's expense -- is particularly obnoxious to the Israelis.
The Jerusalem Post's Washington correspondent reported at the turn of the year that if Mr. Reagan were ''swallowing America's pride and turning the other cheek'' to Mr. Begin, ''it is only because of widespread fears among the Reagan inner circle that the Israeli government is fully capable of unleashing even more surprises in the coming days and weeks.''
But if there has been no progress on the Palestinian issue by the time Israel completes its Sinai withdrawal in April,'' the correspondent continued, ''a greater (US) willingness to get tough with Israel might develop. . . . Reagan's charm and smiles will disappear. He may actually become mean.''
Israel's US ambassador-designate, Moshe Arens, has been even more specific in a Jerusalem Post article: ''In its attempt to woo the Saudi princes, the US has apparently adopted the Saudi approach toward the problems of the Middle East. . . . When Israel completes the withdrawal from Sinai, the US might try to effect similar withdrawals from Judea, Samaria, Gaza, and the Golan by threatening to retract its previous commitments to Israel.'' (Judea and Samaria constitute the West Bank.)
Not only is Mr. Haig likely to find these suspicions close to the surface in his talks with Mr. Begin and the equally hard-line Israeli Foreign Minister Yitzhak Shamir. The suspicions may well have been deepened by the reports from Cairo about no deadline for the autonomy talks and about the possibility of broadening them.
The Israelis may wonder whether that may imply broadening the talks in due course by shifting from the Camp David formula to the Saudi peace plan, with its demand for a Palestinian state.