Tyre, Lebanon — Israel faces tough decisions in the wake of Friday's truck-bomb attack that destroyed a military headquarters here, killing 28 Israelis and 32 Arabs. The key issues:
* What, if any, further military response should be made against Iranian, radical Lebanese, and Palestinian groups suspected of complicity in the raid and against Syria, whom Israel says backed it? Israel's immediate response was two air strikes against Palestinian ''terrorist headquarters'' near the Beirut-Damascus Highway.
* Should the bridges over the Awali River, which divides north Lebanon from the area occupied by Israel, be closed to vehicular traffic? Such a move might ease Israeli security but it would heavily penalize Lebanese civilians and would effectively partition Lebanon.
* Should Israel cut its losses and pull its troops back from south Lebanon, relying on Israeli-backed Lebanese militias and occasional Israeli forays to prevent anti-Israeli forces from returning to the area?
The Israeli Cabinet met in closed session Sunday to hear reports on the Tyre attack, but official sources said it did not decide what to do about the Awali bridges, which have been closed since the incident.
Informed sources say a total Israeli pullback from south Lebanon is not under consideration. Most Cabinet ministers think this would lead to the movement of hostile Palestinian and Lebanese forces back to south Lebanon, where their presence could threaten northern Israel.
Prime Minister Yitzhak Shamir said Saturday that although the government is eager to bring back all the troops, this would be done only after northern Israeli cities are safe from missile fire.
Debate in Israel over having its troop in Lebanon could heat up, especially if - as appears more and more likely - elections are moved up a year to 1984.
There is little agreement in the government over whether to close the Awali bridges and impose tougher security measures in south Lebanon. At least two Cabinet ministers want to stop traffic over the Awali, a move that would disrupt commercial ties with the north. Individuals would be allowed to cross by foot and continue by taxi or bus. Goods from Beirut would have to be unloaded at the river and reloaded onto south Lebanese trucks. This would increase the tendency to import goods through the Israeli port of Haifa and would increasingly tie south Lebanon to the Israeli economy.
Shamir and Defense Minister Moshe Arens are reluctant to close the bridges, fearing that would antagonize local Lebanese, who might then be more willing to shelter terrorists. Closure would also rouse a political furor since, in effect, it would partition Lebanon.
Nevertheless, Israeli military sources say the idea is being considered as a means of combating increasingly sophisticated techniques of smuggling explosives into south Lebanon in specially designed cars. Up to 6,000 cars cross the Awali each way on a busy day.
Army Chief of Staff Moshe Levy said the explosion would force Israel to place restrictions on south Lebanese civilians, an apparent reflection of military pressure for stronger security measures in south Lebanon.
Israeli spokesmen went out of their way to deny Lebanese reports that their planes had hit Syrian positions, a signal Israel is not seeking broad hostilities with Syria. But Israeli statements were also seen as a message to Syria that Israel's weariness with the Lebanese situation would not prevent it from striking if provoked.
The Israelis are aware the United States is hoping for a more assertive Israeli posture against Syria and its Lebanese allies. Israeli officials noted the lack of US criticism of the Israeli air strikes.
Also, the US is increasing the number of warships off Lebanon, reportedly sending two aircraft carriers to join another carrier, one destroyer, and a fleet of other ships, amid speculation that the US may be planning a strike in retaliation for the Oct. 23 bombing of US Marine headquarters in Beirut.