Rahma Ibrahim Abu Shamas was reportedly inside her home in Dair al-Balah in central Gaza on Wednesday when a bullet struck her in the head, killing her instantly.
Palestinian sources said Israeli soldiers manning an army watchtower at the nearby colony of Kfar Darom opened machinegun fire randomly on Palestinian homes around dawn on Wednesday.
An Israeli army spokesman acknowledged the killings, saying the army was looking into the "incident".
The spokesman said soldiers thought that Palestinian resistance activists were present in the neighbourhood.
However, the Israeli-state run radio, Cal Yisrael, said no Palestinians fighters were present in the area when the shooting took place.
PA security officials in the Gaza Strip condemned the killing, calling it "another hideous crime".
Over 650 Palestinian children
have died during the intifada
"Imagine that a Jewish child was killed and how Israel would react. They are killing our children in cold blood," Abu Muammar, a Palestinian security official in Dair al-Balah, said.
Ever since the outbreak of al-Aqsa intifada against the Israeli occupation, the Israeli army and paramilitary Jewish Talmudic settlers have killed more than 650 Palestinian children and minors.
Additional hundreds have been injured or maimed by bullets and shrapnel from artillery shells.
The Israeli army routinely denies its soldiers target Palestinian children.
The Dair al-Balah shooting happened despite an Israeli official announcement on Wednesday that the army would not carry
out any more extra-judicial killings of Palestinian activists in areas where Palestinian police could assure calm and security.
Israel also announced on public radio that it had renewed its political contacts with the Palestinian Authority, six days after announcing a freeze in talks.
The report added that Israeli Prime Minister Ariel Sharon's bureau chief, Dov Weisglass, had scheduled a meeting with Palestinian Negotiations Minister Saib Uraiqat to take place "soon".
"We call upon the Israelis to unconditionally return to the negotiating table so both sides can implement their road map commitments"
Palestinian Negotiations Minister
Sharon announced a freeze in the talks on Thursday, after the 13 January killing of six Israeli security men at a Gaza Strip border checkpoint.
Since then Israeli and Palestinian generals have held two security meetings to coordinate the deployment of Palestinian security forces in the Gaza Strip, but no political meetings had been held.
A senior Palestinian official said he had been in contact with Israeli counterparts for at least the past week, but urged Israel to focus any new negotiations on reviving a road map backed by the UN, the US, the EU and Russia.
Palestinian security forces tore
down illegal structures in Gaza
"We call upon the Israelis unconditionally to return to the negotiating table so that both sides can implement their commitments stated in the road map, beginning with the cessation of violence," Uraiqat said.
Palestinian security forces began deploying in southern Gaza in an attempt to end the firing of rockets by Palestinian resistance groups, under orders from newly elected leader Mahmud Abbas, witnesses said.
They said about 20 officers had taken up positions at the Tufah crossing near a Jewish settlement bloc.
Palestinian police fanned out in north Gaza last week with the Israeli army's agreement, ushering in a calm that Abbas now also wants to establish in the south of the territory.