Israeli aircraft have also attacked a building in Gaza City said to be used by Fatah fighters.
Two armed men and two civilians were killed in earlier fighting on Wednesday in the northern Gaza towns of Beit Hanoun and Jebaliya.
Hospital officials said Israeli soldiers killed two men from Hamas. They also said that a 14-year-old boy died in a refugee camp and a Palestinian woman was killed when Israel shelled an area used by rocket crews.
Israeli troops forcibly entered the home of Jamila Shanti, a Hamas legislator who earlier in the month helped to organise a women's demonstration that let dozens of Palestinian fighters escape an Israeli siege on a Beit Hanoun mosque.
Shanti was not in the house at the time, contrary to Palestinian security officials' earlier reports.
A Palestinian fighter from the Al-Aqsa Martyrs' Brigades was killed and two others seriously wounded in separate raids on the northern West Bank town of Jenin.
The army's operations came after Israel's security cabinet said it would continue its military raids and "targeted killings" in Gaza.
One man was killed as Israeli tanks operated
around the town of Beit Lahiya on Thursday
Some cabinet members wanted Ehud Olmert, Israel's prime minister, to approve tougher action to stop rocket salvos aimed at towns and villages that border Gaza.
A security cabinet statement also called for continued cooperation with Cairo to prevent the smuggling of weapons into Gaza from neighbouring Egypt.
In efforts to arrange an exchange of Palestinian prisoners in Israel for Shalit, Khalid Mishaal, a Hamas leader who lives in exile in Damascus, arrived in Cairo on Thursday to discuss Egyptian mediation efforts for a swap.
Izzat al-Rishq, a senior Hamas member, said: "The delegation, led by Mishaal, will follow up on Egyptian efforts to reach a deal acceptable to the Palestinian people."
Aid work suspended
The Red Cross has meanwhile suspended its activities in Gaza after armed men kidnapped two of its workers, its local office said.
Iyad Nasir, a spokesman in Gaza for the the International Committee of the Red Cross, said the two Italian aid workers were released early on Wednesday and were reported to be unharmed.
Over the past two years, a number of foreign aid workers and journalists have been kidnapped in Gaza, usually by groups or families pressing the government for money or job guarantees. In most cases, the hostages are quickly released and none has been seriously harmed.
Military incursions from Israel into Gaza continue, with Israel saying it wants to stop Palestinian rockets being fired and to release a soldier captured in June.
Israel has killed more than 370 Palestinians in Gaza, about half of them civilians, since it began the offensive.