Washington — Suddenly Washington finds its two top diplomats called overseas to mediate separate crises, both of great import to the United States and the world.
Deputy Secretary of State Walter J. Stoessel Jr., en route to the Middle East , crossed paths briefly in London with his chief, Secretary of State Alexander M. Haig Jr., who was grappling with the Falklands dispute.
Mr. Stoessel's task is two-pronged: (1) to ensure that Israel pulls out of Sinai on schedule April 25 and (2) to urge that Israel not invade Lebanon in a campaign to punish the Palestine Liberation Organization (PLO).
Egypt had urgently wanted Mr. Haig himself to come to Jerusalem and Cairo. Egyptian officials are finding it hard to negotiate meaningfully with Israeli officials in their present mood. Haig, the Egyptians reportedly thought, might be able to ''stabilize'' the Israelis, as one source put it, and ''calm them down.''
With Haig tied up over the Falklands crisis, Mr. Stoessel was the next-ranking official. Pending Stoessel's arrival, Assistant Secretary of State Nicholas A. Veliotes had been on the scene in the Middle East.
Experts here could recall no time in recent history when the nation's two top diplomatic officials - the secretary of state and deputy secretary--were out of the country, coping with separate problems of great magnitude.
Without discounting dangers inherent in the British-Argentine dispute over the Falkland Islands, some diplomats here described events in the Middle East as posing the greater threat to world peace.
War in the Middle East, they said, could have incalculable results, including the collapse of the Egyptian-Israeli peace accord, a threat to the West's oil supplies, and Soviet-American tension, if not confrontation.
Some diplomatic sources said that relative neglect of the Middle East by the Reagan administration, because of preoccupation with Latin America and domestic economic problems, had allowed the initiative to pass into the hands of an increasingly truculent Israeli government.
Israel's recent annexation of the Golan Heights, seized from Syria in 1967, angered the Reagan administration, which retaliated by suspending an agreement calling for broader US-Israeli strategic cooperation. This, in turn, stirred Israeli Prime Minister Menachem Begin to public criticism of the United States.
American officials now have two primary concerns about Begin's policies, as they are perceived here:
* The Israeli prime minister, determined to maintain Israeli control over the West Bank, interprets proposed Palestinian autonomy there differently from the US and Egypt, the other signatories of the Camp David accords.
* Backed by Defense Minister Ariel Sharon and other Israeli hard-liners, Begin--as viewed here--intends at some point to destroy the military capability of the PLO.
This would involve an attack into Lebanon, headquarters of the PLO. While the Israeli Army drove north at least to Lebanon's Litani River and perhaps farther, Israeli sea and air forces might attack Beirut in an effort to kill, or seize, PLO leaders.
At the same time, Israel is considered likely to attack and destroy the surface-to-air missiles which Syria moved into Lebanon a year ago. Presumably, said a diplomatic source with long experience in the Middle East, all this would force Syria to engage Israel, at least in air battles.
At that point Israel might decide to humble its longtime foe, Syrian President Hafez Assad, who has 30,000 Syrian troops in Lebanon in a peace-keeping role assigned to Syria by the Arab League.
A Syrian-Israeli clash could trigger Soviet support of President Assad's regime, though - in previous Arab-Israeli wars--both Moscow and Washington have held back from open confrontation between their own forces in the Middle East.
The view in Washington, meanwhile, is that Israel intends to fulfill its April 25 withdrawal commitment from Sinai, despite Israeli complaints that President Hosni Mubarak's Egyptian government is not living up to its side of the bargain. Specifically, Israeli officials charge Egypt, among other things, with allowing the PLO to smuggle arms into Gaza through Sinai.
Israel also seeks several minor border rectifications, including control of a new luxury hotel west of Eilat on the Gulf of Aqaba.
US officials credit Mr. Begin with courage in evacuating Israeli settlers from Yamit and other Sinai towns, prior to handing over the final slice of the desert territory to Egypt on April 25.
To uproot Jews who had labored to make the desert bloom runs counter to Zionist tradition and was, for Begin, a difficult decision to take. Some diehard Jewish opponents of evacuation remain to be dislodged by the Israeli Army.
Beyond the present turmoil, experts here see a need for the Reagan administration to develop a coherent policy for carrying the Middle East peace process a step beyond Camp David.
The original Haig thesis - a ''strategic consensus'' of the United States, Israel, and friendly Arab states against communist influence in the area - foundered on the rock of Arab-Israeli hostility.
Meanwhile, the Arab world itself is badly splintered, with Jordan and Saudi Arabia backing Iraq in its war with Iran, while President Assad's Syria supports Iran.