At least 29 Palestinians have been killed since the latest spasm of violence erupted on March 20, with 11 killed over the past two days by Israeli action after an attack on a school bus which injured two Israelis including a teenager.
The Israeli military on Friday said it "identified two terrorist squads from Hamas" and hit the militants from the ground and air. A later strike near the coast killed a third militant and wounded another, Gaza medical sources said.
Hamas said a local commander was also badly injured, and it responded by firing six rockets at Israel from the south.
An elderly Palestinian and two women died earlier when their house in Khan Younis was hit and three other women were wounded, according to hospital sources.
An Israel Defence Forces (IDF) statement said "uninvolved civilians have apparently been injured" in one strike.
"The IDF regrets that the Hamas terrorist organisation chooses to operate from within its civilian population, using it as a 'human shield'," the statement said.
At least 15 rockets have been fired into Israel since dawn, causing damage but no injuries, said a police spokesman. Police were restricting traffic near the border area and there appeared to be no early end in sight to operations.