The strikes on Beit Lahiya and Rafah on Thursday followed a similar attack on Wednesday which killed four Palestinian fighters near Gaza City. Israel launched the latest offensive after an Islamic Jihad bomber killed five of its citizens last week.
Witnesses said the three-storey building targeted in Beit Lahiya village belonged to Amer Karmut, a leader of the Popular Resistance Committee (PRC), a coalition of Palestinian fighters that specialises in cross-border rocket fire into Israel.
The building was partly gutted by fire, but the fighter was unhurt. Another Palestinian was wounded, medics said.
An Israeli army spokeswoman confirmed both strikes, saying the first had targeted a structure in Jabaliya refugee camp which was "used by the Popular Resistance Committees for storing weapons".
The second air raid "targeted an office in Rafah used by Islamic Jihad for terrorist activity," she said.
In Rafah, an Israeli aircraft fired a missile at the office of a charity linked to Islamic Jihad, causing damage but no casualties. Military sources said the office had been used to plan attacks.
Earlier on Thursday, Israeli aircraft fired rockets at open areas of northern Gaza used by Palestinian rocket crews to fire into Israel, military sources said. No one was hurt.