The Carter administration's bid to halt permanently the fighting in southern Lebanon is concluding its first phase with U.S. officials privately expressing "cautious optimism" that peace can be restored to the strife-torn area.

These officials stressed that they still don't have a specific plan for shoring up the shaky cease-fire in the region. But they said the first stage of the U.S. diplomatic initiative, which concentrated on exploring the attitudes of the many countries and factions involved, yielded what one official called "reasonable grounds for optimism."

The officials cited as hopeful signs: a feeling of influential Arab countries that the fighting must be stopped before it triggers wider Middle East hostilities, hints from the Palestine Liberation Organization that it might formally agree not to use southern Lebanon as a base for terrorist raids into Israel, and indications of greater Israeli flexibility on ending cross-border retaliatory strikes against the PLO.

Still, the officials admitted, these stirrings, while encouraging, are vague and qualified by conditions and questions that must be answered before a workable peace plan can be devised.

As a result, they continued, the next stage of U.S. initiative will concentrate on specific proposals that can provide the basis for further negotiations on a mechanism for maintaining the cease-fire.

However, the officials, saying it would be foolish for the United States to tie itself to any specific plan before completing its exploratory talks, characterized as inaccurate a spate of recent rumors that Washington has a specific mechanism in mind.

Instead, they said, the administration has only a broad and generalized outline of what it hopes to accomplish through the initiative announced Sept. 25 by Secretary of State Cyrus R. Vance.

The initiative's most immediate goal, they said, is to solidify the uneasy cease-fire so that it will not break down into renewed fighting.

Once that is accomplished, officials hope to tackle the larger problem of defusing Lebanon as a Middle East flash point by restoring the authority of the Lebanese government in the southern part of the country and ending the civil war that has pitted PLO guerrillas and Labanese Moslems against Israeli-backed Christian militias.

This effort has been given a very high priority by Vance and his assistant secretary for Middle East affairs, Harold Saunders. Vance spent much of his time at the United Nations over the past three weeks talking about Lebanon with Arab foreign ministers and representatives of the European countries providing troops for the U.N. Interim Force in Lebanon (UNI-FIL).

In addition, the sources said, Vance also has assigned Philip C. Habib, a former undersecretary for political affairs, as an adviser.

The involvement of Habib, formerly considered the most influential of Vance's subordinates, is deemed a sign of the importance that Vance attaches to the situation.

As a result of Vance's soundings with Arab leaders, the sources said, the United States now is convinced that key Arab countries -- among them Syria, which has sizable forces in Lebanon; Saudi Arabia, a major financial supporter of the PLO, and Kuwait, the current Arab member of the U.N. Security Council -- share the U.S. view that the violence in Lebanon must be ended.

According to the sources, the United States, whose agreements with Israel prevent direct U.S. contact with the PLO, hopes that these countries will press the Palestinian forces to cooperate in permitting more effective implementation of U.N. resolution 425, which created UNIFIL to act as a buffer force along the Israeli-Lebanese border.

Such cooperation would require the PLO to avoid clashes with UNIFIL, to halt incursions into Israel from southern Lebanon, and to agree to negotiate about withdrawing some of its forces from the south.

The sources said the PLO, which reportly has suffered heavy military losses from Israel's retaliatory pounding, has put out vague but discernible hints that it might agree to these conditions if Israel halts its land, artillery and air strikes.

U.S. discussions with Israel have centered largely on contacts by Vance and Saunders with Ephraim Evron, the Israeli ambassador here. The sources said that, in the face of U.S. arguments about the need to strengthen observance of Resolution 425, Israel so far has not committed as retaliation against PLO terrorism, even if the terrorist acts cannot be related directly to southern Lebanon.

However, the officials added, the Israelis, while raising a number of questions, have not rejected the idea or even spelled out their position in any formal, detailed way. At this time, the officials said, the Israeli stance can best be described as one of "flexibility and listening" rather than negativism.