In the latest strike, an unmanned Israeli drone fired a missile at a group of gunmen as they clashed with Israeli ground troops in Beit Hanoun, in the north of the Gaza Strip, killing two militants and wounding two, witnesses and medics said.
An Israeli army spokesman confirmed the attack and said it had been ordered after Israeli troops saw militants trying to plant a bomb in the area.
Earlier, an Israeli air strike killed three gunmen in Beit Lahiya, a district not far from Beit Hanoun. The army said it had opened fire on a group of men seen carrying an anti-tank grenade launcher. Witnesses said about 10 Palestinians were wounded in the strike.
The attacks were carried out shortly after Israeli tanks, backed by helicopters, moved into farmland near Beit Hanoun, from where militants often fire homemade rockets into Israel. Israeli forces had pulled out of the area just a week ago.
Medics said Israeli forces killed a Palestinian woman in a separate operation in southern Gaza, where Israeli troops have been based since late last month as part of an operation to rescue an Israeli soldier captured by militants.
Witnesses said an Israeli tank shell landed near the woman's house, sending shrapnel flying inside and killing her. The army denied firing any tank or artillery shells in the area.
Rafah border crossing
Israel began its Gaza offensive after militants, some from Hamas, captured Corporal Gilad Shalit in a cross-border raid on June 25. The Israeli military has since killed more than 85 Palestinians in Gaza - about half of them militants.
Gunmen blew a hole in the border
wall to let 1,000 people into Gaza
Hamas, which controls the Palestinian government, is demanding that Israel free Palestinian prisoners in exchange for Shalit's release. Israel has rejected any exchange.
Israeli aircraft also hit a Hamas office in the Islamist stronghold of Jabalya. Israel has damaged several structures belonging to Hamas and the government it heads, including the office of Ismail Haniyeh, the prime minister.
Palestinian officials said the Rafah border crossing between Gaza and Egypt would re-open for one day- on Tuesday - to allow Palestinians who were stranded by the closed border to cross home.
On Friday, Hamas gunmen blew a hole in the border wall, allowing nearly 1,000 Palestinians to return to Gaza.