The Lebanese government has agreed to allow Israeli soldiers to play a limited role in helping Lebanese troops supervise security arrangements in southern Lebanon as part of a proposed agreement on Israeli withdrawal from that country, well-informed sources said today.

Yesterday, U.S. Secretary of State George P. Shultz carried the draft of the proposed accord to Israel, where the Cabinet was scheduled to consider it Friday. It was unclear, however, whether the Lebanese concessions went far enough to satisfy the government of Prime Minister Menachem Begin.

In Jerusalem, U.S. officials who accompanied Shultz on his week-long diplomatic shuttle between Jerusalem and Beirut said that they were "cautiously optimistic" that the Begin government would approve the agreement, Washington Post Staff Writer John M. Goshko reported.

Intense speculation gripped Israel over how Begin would react to expected heavy opposition to a Lebanese withdrawal from Cabinet hard-liners led by former defense minister Ariel Sharon. Much of the speculation centered on predictions that the Cabinet would be too divided to achieve an immediate consensus and might postpone a decision or ask Shultz to return to Beirut in search of further concessions from Lebanese President Amin Gemayel.

Israeli negotiators had sought creation of joint Israeli-Lebanese combat patrols with powers to interdict guerrillas, but the sources said that the Israeli side had agreed tentatively to allow the Lebanese Army to carry out security and police functions in the south.

In a refined version of oral accords reached earlier, the Israeli negotiators reportedly agreed that the mission of joint Israeli-Lebanese "supervisory teams" would be limited to "verification and reporting" on security in a zone extending between 15 and 18 kilometers (9-11 miles) north of Israel's border.

Israeli troops in the teams would be under the command of Lebanese officers and allowed to move only in Lebanese military vehicles, the sources said. An Israeli-Lebanese liaison committee would determine the teams' activities and size, with representatives of either country able to veto any proposal.

The sources also said that one key issue--the future status of Israeli-allied militia commander Saad Haddad--has not been resolved. Israel wants the former Lebanese Army major to command Lebanese Army forces in the south, while the Lebanese have indicated that they would agree only to give him an honorary post of deputy commander while vesting executive powers in the hands of another commander.

According to well-placed sources here, Shultz personally is handling the Haddad matter in dealings with Begin and Gemayel. The sources said that the issue is not addressed in the draft accord but that an understanding is to be reached on it before an agreement is signed.

Lebanese negotiators were guardedly optimistic about the fate of the agreement.

"We have made many concessions, and so have the Israelis," one member of the Lebanese negotiating team said. "But the implementation will be more difficult than the drafting because of the Syrians."

If Syria objects to the Israeli role in the south or to other provisions of the accord, it could refuse to withdraw its forces from Lebanon and thus lead Israel to refuse to pull out its troops.

Shultz is to go to Syria Saturday in his shuttle diplomacy efforts, and the Lebanese negotiator predicted that "the meeting in Damascus will be very, very difficult."

Syria's state-run radio warned Beirut to reject any agreement that "will paralyze Lebanon's sovereignty and threaten Syrian and Arab security," United Press International reported. The radio condemned the Shultz-mediated draft agreement, charging that it would grant Israel the right to invade Lebanon again.

The issue of normalization of relations between Lebanon and Israel is not addressed in the draft accord, according to the sources, although there are hints in it that the matter would be taken up six months after troop withdrawal.

An umbrella committee of Americans, Israelis and Lebanese is established in the agreement to oversee implementation of the accords. There were reports that there still was disagreement over whether it should be located in southern Lebanon, as the Lebanese prefer, or in the Beirut area, presumably the desired location of the Israelis.

In order not to give the impression that this committee is a version of a mini-embassy including Israel, the Lebanese reportedly have decided not to confer full diplomatic status on its Israeli representatives.

United Nations peace-keeping forces already in the south would help Lebanese troops protect Palestinian refugee camps under the tentative accords. No role is assigned there, however, to troops in the multinational peace-keeping force in Beirut consisting of U.S., French, Italian and British contingents.

Staff writer Goshko added the following from Jerusalem:

U.S. officials stressed that Shultz believes that the Lebanese have gone as far as they can to accommodate Israel. In addition, the officials said, Shultz made clear that he would be very disappointed if there were not an Israeli decision before he leaves Jerusalem Friday afternoon to consult with Arab leaders about Lebanon and the broader Middle East peace process.

The secretary will go first to Amman for talks with Jordan's King Hussein about the possibility of getting Reagan's Middle East peace initiative back on track.

On Saturday, Shultz will go on to Damascus to discuss the Lebanon agreement with Syrian President Hafez Assad. Later that day, Shultz will go to Riyadh for a meeting with King Fahd of Saudi Arabia. On Sunday, he will return to Israel briefly to advise the Israelis of his talks in the Arab capitals and then fly to Paris for an economic meeting.

Shultz spoke by telephone for 15 minutes with Reagan. U.S. officials said the call was to give the president Shultz's assessment of the situation and insisted that it was not necessitated by any last-minute hitches requiring Reagan's personal attention.

Reagan, questioned in San Antonio about prospects for a Lebanese-Israeli agreement, said, "We've got a no-hitter going, and I don't want to say anything to jinx it." Asked if prospects were good, Reagan held up crossed fingers and said, "Yes."