The lull in the fighting in Lebanon is a direct consequence of mistaken assumptions on the part of the Reagan administration in Washington and the Begin Cabinet in Jerusalem.
The Reagan administration wrongly assumed it could accept Israeli Prime Minister Menachem Begin's assurances about the limited aims of the Israeli invasion of Lebanon launched June 6. The Israeli forces, it was initially said, were clearing a 25-mile wide buffer zone free of Palestinian guerrillas along Israel's northern border. In fact, Israeli forces are now laying siege to western Beirut and threatening to storm it.
Secretary of State Alexander M. Haig Jr.'s resignation is part of the price being paid for this mistaken assumption. Within the Reagan Cabinet, he had argued for acceptance and sympathetic understanding of the Israeli line.
The Begin Cabinet wrongly assumed that if Israeli forces could put a noose around the 6,000 fighters of the Palestine Liberation Organization (PLO) in west Beirut, the right-wing Christian Phalangist militia of Bashir Gemayel -- a discreet ally in the past -- would be willing to move in and perform the unpleasant task of finishing the trapped Palestinians off.
The Phalangists' move made it clear they will do no such thing -- apparently because Mr. Gemayel assumes being seen too openly as Israel's mercenary and puppet would prejudice his chance of being Lebanon's next president.
''We will not be involved on a military level,'' a Phalangist spokesman told a Washington Post correspondent. ''We are trying to profit from this situation on a political level only.''
This has not prevented the Phalangists from militarily taking advantage of situations resulting from Israeli actions -- such as moving into communities on the Beirut-Damascus highway cleared by the Israelis of Syrians and Palestinians. But they are refusing to initiate major action of their own against the PLO.
The governments of both the US and Israel are weighing separately their next moves now that their earlier calculations have proven faulty.
There are some signs that the Reagan administration is moving toward a tougher stand in its dealing with Israel -- despite a US veto in Israel's behalf in a United Nations Security Council vote at the weekend.
The Hearst newspaper chain's John Wallach, usually well-informed on the Middle East, reported that even before the Haig resignation President Reagan had asked Mr. Haig to warn Israel to accept the latest deal for a Lebanon cease-fire worked out by US special envoy Philip Habib or face the certain threat of a US arms cutoff.
(The Israelis did accept a cease-fire in the Beirut area late June 25 and, unlike three earlier cease-fires, this latest one was still holding June 27.)
In Jerusalem, the Begin Cabinet announced June 27 that it would maintain the cease-fire, but would open fire if fired upon.
The Cabinet also considered proposals worked out in Beirut by Mr. Habib whereby the trapped PLO men would be brought under outside control in a face-saving way.
After the Cabinet meeting, it was reported the government was insisting the PLO surrender its arms to the Lebanese Army and then be escorted from western Beirut (under safe-conduct) out of Lebanon along the Beirut-Damascus highway, into Syria.
Syria's relations with the PLO have always been equivocal at best, despite a smoke screen of rhetoric. Whether either the PLO or Syria would voluntarily accept any such transfer of base and personnel to Syria is very much open to question.
It appears that the announcement after the Israeli Cabinet meeting may have included conditions that are expected to be rejected. As if to confirm this, Israeli aircraft dropped leaflets over Beirut June 27 saying the war with the PLO was not yet over. The leaflets advised Lebanese of routes to leave the city while the cease-fire lasted.
As Israeli hard-liners see it, their military operations in Lebanon present an unprecedented opportunity to destroy the PLO once and for all with a single blow. They are so close to this now that they believe it would be foolhardy to allow themselves to be stopped in their tracks.
Israel's brilliant but ruthless and swashbuckling defense minister, Ariel Sharon - pacesetter till now for the Israeli operations inside Lebanon - said on Israeli television just before the June 25 cease-fire went into effect: ''We should not be affected by any political provocations, internal or external, that exist and may threaten our military and political achievements.''
Presumably he was referring to pressure from the US - the only pressure that really counts with the Israelis - or from the Europeans or the UN.
The Israelis may also want to present the US with a fait accompli in Lebanon before incoming Secretary of State George Shultz takes over from Alexander Haig. They are worried lest Mr. Shultz prove less sympathetic toward them than was Mr. Haig. They suspect Mr. Shultz of pro-Arab, and particularly pro-Saudi, sympathies because he is coming to the State Department from the presidency of the San Francisco-based Bechtel Corporation which has been involved in Saudi Arabia.
Saudi Arabia and Egypt, seen by the Reagan administration as moderate Arab allies, reportedly renewed their representations in Washington at the weekend for US action to halt the Israelis in Lebanon. Both countries expressed their dismay at the latest US veto in Israel's behalf in the UN Security Council.
The Hearst chain's John Wallach reported that when President Reagan reminded Prime Minister Begin over lunch June 21 that the US must remember its moderate Arab allies such as Saudi Arabia and Jordan, Mr. Begin retorted with an attack on the ''corrupt, unstable dictatorship'' represented by the Saudi royal family.
As for Jordan, Mr. Wallach said (on the public television program ''Washington Week in Review'') that Mr. Begin had bluntly told Mr. Reagan that Israel would see as a mortal threat any honoring by the US of King Hussein's request for F-16 jet fighters and mobile Hawk surface-to-air missiles.
President Reagan was so affronted, Mr. Wallach said, that he deliberately omitted a toast he had intended proposing to his Israeli guest.