JERUSALEM, OCT. 12 -- A Palestinian mother on her way to pick up some of her children was shot dead today when Israeli soldiers opened fire with Uzi submachine guns on a stone-throwing mob in the crowded main square of the West Bank city of Ramallah.

Five other Palestinians were wounded in the incident, which occurred on the sixth day of rioting in the Israeli-occupied territories. The trouble, which began with a shoot-out between Israeli security forces and Arab gunmen in the Gaza Strip last week, has spilled over into the West Bank and Jerusalem.

Israeli military officials acknowledged that the woman was an innocent bystander and said they regretted her death but contended that two soldiers and four Israeli policemen were trapped by the crowd and their lives were threatened when they opened fire.

The incident in Ramallah, about 15 miles north of Jerusalem, began this morning around 8 a.m. Several hundred schoolchildren left their classes and began a demonstration in Manara Square, the city's main commercial center, to protest yesterday's clash between Moslems and Israeli police at the sacred Temple Mount in East Jerusalem. The students threw up roadblocks, chanted Palestinian slogans and began throwing rocks at cars with yellow Israeli license plates.

According to the Army's account, one car's windshield was shattered and a woman passenger was lightly injured. A police vehicle that came to the car's rescue was pelted with rocks as was an Army vehicle with two soldiers.

The Israelis said they were surrounded by the students. who refused to disperse when they shouted warnings, according to the military account. They then aimed at the legs of the demonstrators and opened fire with the Uzis.

One of those hit was identified as Amayat Samir Hindi, a school teacher who was shot in the chest and was dead on arrival at Ramallah Hospital. Israeli military officials said a preliminary investigation indicated she had been passing through the area and was not involved in the disturbance.

Staffers at the hospital said her husband told them she had been on her way to the market to buy bread when she saw the demonstrators and decided to retrieve some of her children from school and take them home, away from the disturbances. She was shot on the way.

An Army official who asked not to be identified said the preliminary investigation indicated that the soldiers had fired single shots from their Uzis. But witnesses at the scene told reporters they heard rapid-fire shooting, suggesting that the soldiers sprayed the crowded commercial center with bullets.

The Army commander of the area, who under military rules cannot be identified, told Israel Army radio that he regretted the woman's death, "but you have to realize that when soldiers get in a situation like that and have to open fire to extricate themselves, other people may get hurt."

All shops closed in protest throughout Ramallah, and many stores were closed in East Jerusalem and Gaza.

Gaza and the West Bank periodically erupt in violent clashes reflecting Palestinian frustration with Israeli military occupation. The disturbances tend to burn themselves out after several days, but this time Israeli actions have helped to sustain them.

The latest round began two weeks ago when three Arabs were gunned down by soldiers in Gaza after allegedly running a military roadblock. It was exacerbated by last week's shoot-out, which involved members of the Islamic Jihad, a Moslem extremist movement -- giving a religious dimension to the violence.

The shootings set off protests in Gaza and shop closures. Soldiers shot at people throwing stones Saturday, wounding at least six, and tried to force shopkeepers to reopen yesterday.

Then yesterday a small group of Jewish nationalists sought to enter the Temple Mount, a holy site for both Arabs and Jews and site of two mosques. That set off a clash between police and Moslem protesters.

Today's shooting is certain to fuel the conflict further, and many expect it to continue at least through the weekend, when Secretary of State George P. Shultz arrives in Israel for a visit.