Aljazeera's correspondent in Gaza said Israeli troops killed Rahma Abu Shamas and injured three Palestinian civilians in Dair al-Balah region of the central Gaza Strip on Wednesday.
The shootings came as an Israeli official announced on Wednesday that the army would not carry out any more "targeted liquidations" of Palestinian activists in areas where Palestinian police could assure calm and security.
Tel Aviv 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".
Call for negotiations
Sharon announced a freeze in the talks on Thursday, after the 13 January killing of six Israeli security employees 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.
"We call upon the Israelis to unconditionally return to the negotiating table so both sides can implement their commitments stated in the road map, beginning with the cessation of violence"
Palestinian negotiations minister
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.
"We call upon the Israelis to unconditionally return to the negotiating table so both sides can implement their commitments stated in the road map, beginning with the cessation of violence," Uraiqat said.
Palestinian police deployment
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 wants to establish in the south of the territory.