Hospital officials named the militant killed in Gaza City's Zeitoun district as Aiman Hassanein, a senior member of the governing Hamas faction. Witnesses said his brother was detained by troops.

A 70-year-old Palestinian woman was shot dead in the Zeitoun clashes, hospital officials said. It was not immediately clear who had fired at her.

An Israeli military spokeswoman confirmed an operation was under way in Zeitoun but did not give further details.

Israeli forces also entered the nearby refugee camp of Jabalya as well as Beit Lahiya, a northern Gaza town frequently used by militants to launch cross-border rocket salvoes.

Israel has intensified its raids in Gaza since militants captured an Israeli soldier in a cross-border raid in June.

Israeli forces have killed more than 370 Palestinians in Gaza, about half of them civilians, since it began the offensive, Palestinian medical officials and residents say.

Three Israeli soldiers have been killed and a woman in an Israeli border town died in a Palestinian rocket strike.

Israeli Defence Minister Amir Peretz said on Monday Israel would press its fight against Palestinian militants firing rockets against the Jewish state but had no intention of reoccupying Gaza, which it quit last year.

"I emphasise that our hand is outstretched in peace, but anybody who rejects it ... should know that ... we will do all we can to sever the hand which uses terror," Peretz said in a speech carried by Israeli radio.