Egypt relayed to Israel two appeals from the Palestine Liberation Organization for a swift cease-fire in Beirut today, Israeli officials reported. But Defense Minister Ariel Sharon strongly indicated that his troops instead may get orders to hunt down PLO leaders at their headquarters inside the Lebanese capital and "deal them a near-mortal blow."

The first cease-fire request was communicated early this morning to Foreign Minister Yitzhak Shamir by the Egyptian ambassador to Israel, Saad Murtada, the officials said. It marked the first time PLO leaders have directly appealed for an end to the fighting and the first time Egypt--ostracized in the Arab world for its peace with Israel--has served as a channel between the guerrilla organization and the Israeli government, they added.

A second PLO appeal was conveyed by Murtada later in the day to the Foreign Ministry's director general, David Kimche, after Shamir had departed for France on a previously arranged visit, the officials reported.

The willingness to deal with Egypt despite its "treason" of the Arab cause and to take the initiative in trying to get Israel to halt its advance was interpreted by Israeli Foreign Ministry officials as an indication that the guerrillas find themselves "in a very difficult position" under Israeli guns.

Shamir, in an oral reply to Murtada, said Israel twice has declared its willingness to cease fire and will halt combat as soon as Palestinian guerrillas stop firing at Israeli soldiers in Lebanon, the officials said. Kimche gave a similar reply to the second Murtada message, they said.

Sharon, who commands the Lebanon operation, told Israeli radio that his troops now command all exits from Beirut through "a massive Israeli Defense Forces presence at all roads leading to Beirut." The government must now decide, he added, whether to dispatch troops inside the city to destroy the PLO leadership.

"There are still thousands of terrorists," he said. "There are still command headquarters. Although they have been destroyed, their commanders found shelter in other places. We must consider how to solve this problem.

"You must understand that the political infrastructure of the terrorist organizations is located in Beirut. At present we have no definite plan. Neither has the Cabinet determined that we should enter Beirut. And so there is no plan to enter Beirut. This is a subject we will have to consider."

Sharon seemed to be hinting at the possibility of a commando-type operation aimed at killing or capturing Yasser Arafat and his lieutenants in the top PLO leadership. The guerrilla chiefs have their headquarters in densely populated quarters of West Beirut or sometimes work from bunkers inside nearby Palestinian refugee camps. Given their present advantage, Israeli troops could easily mount such an assault, although bloodshed among Israelis, Palestinians and Lebanese civilians probably would be high.

"We mean to do only one thing," Sharon said, "to destroy the terrorist infrastructure and deal them a near-mortal blow."

Shamir, departing for Paris, reiterated previous government policy that Israeli troops have no plans to capture Beirut. He said nothing of the kind of operation hinted at by Sharon, however. With Shamir gone and Prime Minister Menachem Begin departing for Washington Tuesday, it was unclear how the Cabinet would decide what to do next in Beirut.

Since the Israeli invasion June 6, Israeli officials have on several occasions defined objectives that later were overtaken by events on the battlefield. Begin first said the operation was to gain a 25-mile guerrilla-free zone in Lebanon, for example, but then Israeli troops advanced farther north to control Beirut. Spokesmen later said there were no plans to link up with Lebanese Christians, but the linkup took place last night with Sharon himself present in Beirut.

In another example, a military spokesman speaking on a radio broadcast denied reports from Beirut that Israeli troops had taken over the Lebanese presidential palace at Baabda overlooking the capital. The next item on the broadcast was a report from an Israeli reporter--telephoning from inside the presidential palace.

Israeli officials also criticized reports from Beirut saying civilian casualties have been mounting. These reports--from the Lebanese Red Cross and an International Red Cross Committee envoy--are "out of proportion," one official said, suggesting they originated from Palestinian sources.

The official declined to give an Israeli estimate of casualties. A Red Cross official in Beirut has said up to 1,500 persons were killed and more than 3,000 wounded during the battle for Sidon alone. Some Lebanese security sources have said up to 15,000 Lebanese and Palestinians have been killed in the week's battles. In past Beirut violence, reports from the security sources often have been imprecise.

Israeli officials, while seeking to play down the extent of civilian casualties, also are pointing to Palestinian weaponry and hostility toward Israel as justification for the massive assault and the casualties that have accompanied it.

"It is a fact that we found that this is the area where they were making preparations for the final destruction of Israel," said one official.

To boost Israel's image in the face of criticism abroad, the foreign minister has dispatched two reserve lieutenant generals and the head of the Israeli broadcast authority to the United States for a round of meetings with editors, television talk shows and speaking appearances. Deputy Foreign Minister Yehuda Ben Meir has traveled to London on a similar mission, a ministry spokesman said.

Although criticism at home has been muted, the opposition Labor Party declared today after a special meeting that it cannot support the government's decision to bomb populated targets such as refugee camps where civilian casualties are likely to be high. At the same time, the party announced it will not criticize the expansion of the government's original objectives in the invasion from protection of northern Israeli setttlements to destruction of the PLO as an oganization.