A threat of renewed war in the Middle East adds to the challenges facing the Reagan administration as it works against time to head off hostilities between Britain and Argentina over the Falkland Islands.
As of this writing, the immediate danger was that Israel might conclude US preoccupation with the Falklands makes the moment favorable for a bold military strike into southern Lebanon. The purpose: to smash once and for all the Palestine Liberation Organization (PLO).
Israeli Prime Minister Menachem Begin may feel all the more tempted to strike now because of:
* The increased uncertainties in the Arab world in the wake of Iran's successful offensive against Iraq after many months of stalemate in the Gulf war.
* Egypt's inhibition against any move to counter an Israeli offensive in Lebanon lest that move give Israel a pretext not to honor its commitment to complete the return of Sinai to the Egyptians April 25.
Fearing an Israeli attack, Lebanon appealed at the weekend to both the United States and the Soviet Union to intervene to stave it off. A White House spokesman with President Reagan in Barbados April 10 said the US was calling on ''all those involved to show the maximum restraint.''
Those most directly involved are the Israeli government and the PLO, between whom in southern Lebanon US special envoy Philip C. Habib last summer negotiated a cease-fire.
Mr. Habib was back in the area last month. The Israelis assured him they would honor the cease-fire unless provoked.
In recent weeks there have been acts of Palestinian violence against Israelis--most notably the assassination of an Israeli diplomat in Paris. Many wondered whether the Israelis would consider this the kind of provocation justifying their moving into southern Lebanon against the PLO.
But these acts of violence were the work of splinter groups under the PLO umbrella. The mainstream PLO group, Al-Fatah of PLO leader Yasser Arafat, disclaimed responsibility for them. At the weekend, however, the Israelis reported they had caught an armed two-man guerrilla squad from Al-Fatah after it had crossed into Israel from Jordan. It remains to be seen whether this is adduced as ''provocation.''
(Adding to tension in the area, a man dressed in Israeli Army fatigues and reported to be a Jewish American, opened fire with an automatic rifle in the Temple Mount area of the Old City of Jerusalem April 11. One Arab was killed and 23 people were taken to the hospital. The man, apparently mentally disturbed, was eventually seized by Israeli security personnel.)
If the Israelis move into southern Lebanon, there is the risk of their clashing with the Syrian forces stationed there--up to 30,000-strong--as part of the so-called Arab peacekeeping force.
Syrian President Hafez Assad recently weathered a storm at home in which his troops moved ruthlessly against the fundamentalist Muslim Brotherhood in the city of Hama. He has turned against another threat to himself--from Iraqi strong man Saddam Hussein. The latter has been shaken in recent weeks by the setback dealt him by Iran's successful offensive against his forces in the war he launched 19 months ago at the head of the Gulf.
Mr. Assad has closed the Syrian border with Iraq and stopped the flow of Iraqi oil through the pipeline that takes it across Syrian territory to terminals on the Mediterranean coast. Iraq depends on transit across Syria not only for its oil exports but also for truck traffic to and from Mediterranean ports.
The Syrian President is the only Arab leader in the Middle East who backs Iran in the Gulf war. He has long been daggers-drawn with his Iraqi opposite number, Saddam Hussein. (Ironically, Israel is with Syria in favoring Iran over Iraq in the Gulf conflict.)
Saddam Hussein is not the favorite of most other Arab leaders, but they prefer him and what he stands for to Iran's brand of Shia Muslim fundamentalism personified by Ayatollah Khomeini. These Arab leaders would thus be in a dilemma if faced with the question of how far to go in support the pro-Iranian Mr. Assad if the latter gets involved with Israeli forces in Lebanon.
Against this background, it is interesting to note that Egypt--a pariah to virtually all Arab leaders since its peace treaty with Israel--seems to be edging back toward acceptability among them. Kuwait opened its doors last week to allow the Egyptian ambassador to the United Nations, Ahmad Esmat Meguid, to attend a meeting of the nonaligned movement. And Mr. Meguid managed to persuade the meeting to drop from its final communique a form of wording specifically condemning his country's peace treaty with Israel.