Israeli troops briefly eased their grip on the northern town of Beit Hanoun, but as darkness fell soldiers began house-to-house searches for militants, local residents said.
The 12-year-old girl was killed by a single bullet to the head, local hospital workers said.
An Israeli army spokesman said a sniper had spotted an armed militant and had fired at him but that apparently the girl was killed as the armed man got out of the line of fire.
He said the army would investigate the matter.
Another man, said to be a 38-year-old civilian was also shot dead by sniper fire, local residents said.
An Israeli army spokesman said troops identified hitting an armed man who tried to approach soldiers in the area.
Earlier, a gunman was killed in battles with Israeli soldiers backed by tanks near Beit Hanoun, home to some 30,000 Palestinians, witnesses said. Militants fired anti-tank rockets at troops, they added.
The army said one soldier was seriously wounded.
The violence came a day after Israel killed 17 people, about half of them civilians, including two women acting as human shields between troops and gunmen hiding in a mosque in Beit Hanoun. Israel's army said it only fired at armed Palestinians.
Israel says the operation, one of the biggest since the army and Jewish settlers pulled out of Gaza last year after 38 years of occupation, aims to halt rocket fire at the Jewish state.
The violence has scuttled hopes of any resumption of peace talks between Israel and the Palestinians, already a remote prospect since the Hamas militant group took power in March following elections. Hamas is sworn to Israel's destruction.
Among the dead on Saturday were two Hamas militants, killed in a missile strike near the Jabalya refugee camp, medical officials said. The army said it was checking the report.
Some 14 Palestinians were wounded in various strikes and clashes, hospital officials added. An 18-year-old civilian wounded by Israeli gunfire earlier on Saturday, later died in hospital, medical workers said.
Three men wounded in the fighting since the offensive began on Wednesday also died of their wounds, hospital workers said.
Israeli forces have killed 45 people in the four-day assault, the Palestinian Health Ministry said.
Beit Hanoun has been under effective curfew since troops moved in, residents say.
A senior aid worker for the United Nations Relief and Works Agency, one of the main assistance providers for Palestinians in the Gaza Strip, said Israel had allowed an aid convoy through to the town earlier in the day to distribute basic aid.
"The situation is very bad for the residents, there is no electricity and the water rationing already in effect is not functioning," John Ging told Reuters.
HUMAN SHIELDS
The Beit Hanoun operation is part of a broader offensive launched in late June following the abduction of an Israeli soldier by militants in a cross-border raid from Gaza.
Since the start of that offensive more than 300 Palestinians have been killed, half of them civilians, hospital officials and residents say. Three Israeli soldiers have been killed.
A Hamas source said Israel had killed 99 of their gunmen since the start of the offensive following the abduction of corporal Gilad Shalit.
Palestinian President Mahmoud Abbas, a moderate who favours peace negotiations with Israel, condemned the killings of the two unarmed women in Beit Hanoun and demanded immediate UN intervention in the conflict.
The Israeli army said it was investigating whether it had shot the women, adding it did not target civilians.
Palestinian militants have fired around 300 home-made missiles at Israel this year from Gaza, Israel says. They are rarely deadly.

Copyright Reuters, 2006