Egypt and Israel tossed sharp verbal barbs at each other as negotiations on Palestinian autonomy resumed today, but then quickly settled down to painstaking discussions on how to approach the thorny issues confronting them.

The session in this Mediterranean city was the second round in talks aimed at autonomy in Gaza and the West Bank called for in the Egyptian-Israeli peace accords signed in Washington March 26.

Although the outlook on all sides is for tough, protracted bargaining with little but technical details discussed at the outset, the ultimate results of these talks will go a long way toward determining the long-run outcome of the Camp David formula for peace in the Middle East.

The bitter atmospherics at the opening today underlined the suspicion, resentment and deep-seated political differences that will have to be overcome if the talks are to reach their goal of an elected self-governing Palestinian authority in the two Israeli-occupied territories.

The Israeli delegation headed by Interior Minister Josef Burg arrived smarting over an editorial in a Cairo newspaper this morning that referred to Prime Minister Menachem Begin and his government as "snakes."

Chastised by Burg, Egyptian Prime Minister Mustafa Khalil retorted that the Israelis had clouded the "atmosphere of peace" by "threats." Their exchange took place in an open session, in front of the press, as their delegations gathered with an American team around a conference table in a steaming mauve and gold room at the San Stefano Hotel.

Egypt wanted the talks to be held at Alexandria's only first-class hotel, the Palestine, but the Israelis let it be known that they were uncomfortable at the connotations of the name.

Burg, Khalil and other members of the three delegations said after two working sessions that they had made progress on what they all described as "procedural" issues, such as formation of committees, the schedule of future meetings and what kind of records to keep. If those seem like mundane matters to be discussed at this level, it is because the issues in the Palestinian autonomy negotiations are so volatile that it is difficult to separate procedure from substance and every point takes on political significance.

Conference sources said that some points were put aside as too sensitive to raise at this time but would not say what they were.

Burg and Khalil spoke jovially with reporters at the end of tonight's session and there was no sign of their earlier antagonism. It appeared, according to participants, that their public statements would not affect the course of the negotiations - which are going to be difficult enough without personality clashes.

Participants in the talks said they were far from approaching the real issues that will face them, such as the scope of Palestinian autonomy and whether the Arabs of East Jerusalem can participate in elections to be held next year, and are certainly not at the point of changing their well-known positions on any of them.

Khalil said is had been agreed to hold negotiating sessions every two weeks and discussion of issues "will come gradually after that." Burg said laughingly that there was nothing in today's sessions to "gladden the heart of the press."

The sharp exchange between Burg and Khalil was provoked by a front-page editorial in this morning's Al Akhbar, Egypt's biggest daily, written by chief editor Moussa Sabri. Sabri known for his intemperate language about whichever country or leader is in disfavor with President Anwar Sadat, condemned Israel for policies that he said would leave these negotiations "stillborn," such as new settlements in the occupied territories.

Sabri said it was time for the United States to intervene against Israel to "lop off the head of the snake before it spews out its venom," and specified that he meant "Begin and the other snakes in Tel Aviv."

When the Israelis took their places at the round table, Borg read a prepared statement in which he said, "Certain publications and utterances are not conducive to creating an atmosphere of peace."

"Talk of snakes and vernom can be poisonous," he added.

Khalil replied that statements in the press "over which we have no control" were not so bad as "a kind of threat of using force or occupying land" from "official responsible minister" in Israel.

This was a reference to remarks by Begin and Defense Minister Ezer Weizman at the recent convention of the Herut Party. Begin said that if a Palestinian autonomy council were to declare independence, the Israelis would reassert their authority in the territories and arrest the members. Weizman, in a statement that particularly upset the Egyptians, was quoted as saying that if it became necessary Israel would once again seize the Sinai.

Khalil said such statements "hurt when they come from friends whom we have faith in."

The acting head of the U.S. delegation James Leonard, caught in the middle, said that the time has come when "public discussion should come to an end" and negotiations should take place "behind closed doors."

Leonard is a professional diplomat and both Egypt and Israel accepted that as the correct diplomatic approach but it may not be possible for them to stick to it as the real irritants enter the negotiations.