The United States has undertaken a diplomatic initiative with Israel, Arab nations and other interested countries in an effort to shore up and extend a cease-fire in sourthern Lebanaon, diplomatic sources said today.

The U.S. contacts followed Secretary of State Cyrus R. Vance's statement to the General Assembly Monday that Washington seeks "not only a cease-fire, but a broader truce" in Lebanon. American sources said the United States fears that intensifying military action by all sides could destroy any semblance of restraint and generate more serious hositlities in the area.

The United States and Israel have agreed that discussions on the question will take place between Assistant Secretary of State Harold Saunders and Israeli Ambassador to the United States Ephraim Evron, as well as between U.S. Ambassador-Samuel Lewis and the Israeli government in Jerusalem, according to State Department spokesman Hodding Carter.

Vance had hoped to discuss the matter with Israeli Foreign Minister Moshe Dayan in a meeting here this morning, but U.S. sources said this was not possible because their entire hour together was consumed by a discussion of arrangements for supervising Israeli withdrawal from the Sinai under the Camp David accords.

Diplomatic sources said the United States has taken up the situation in Lebanon with the Lebanese and Syrian governments and with Kuwait, which is currently the Arab member of the United Nations Security Council. The contacts have taken place both here and in the three Arab capitals in the past several days.

In addition, the United States is taking the issue to the eight nations that have contributed a total of 5,700 men to the U.N. interim peace keeping force in Lebanon.Israel has stymied efforts by the U.N. force to deploy along tthe Israeli border with Lebanon in accordance with its U.N. Security Council mandate by installing rightist Christian militiamen in fortified positions along strip just north of the boarder. The U.N. forces have clashed with Palestinian guerrillas and come under fire from the Israeli-backed Christian militiamen on a number of occasions.

The United States is reported to be seeking the exertion of maximum influence by a variety of nations on the Palestine Liberation Organization, Lebanese Christian forces and Israel to halt a slide toward wider conflict by agreeing to stronger and more permanent arrangements.

Specificially the United States is asking that PLO guerrillas withdraw from south Lebanon instead of infiltrating there in larger numbers.

Despite Israeli efforts to drive guerrillas out, the PLO and other Palestinian guerrilla groups still have thousands of fighters in the South. Agreements with the Lebanese government to limit the presence of Palestinian guerrillas to specifice areas in Lebanon have never been honored by the Palestinian groups.

At the same time, the United States wants Israel to stop its air attacks on southern Lebanon. The raids have devasted villages, forcing Lebanese civilians to flee, and raised tension in the area. Israel has said the strikes are intended to prevent Palestinian commandos from staging raids against the Jewish state.

Dayan, following the meeting with Vance, defended the raids under questioning by reporters. He said Israel cannot wait until attacks are launched and Israelis are killed or wounded before taking action.