Two Palestinians have been killed in fighting with Israeli troops in the northern Gaza Strip.
The foreign ministry building has been almost completely destroyed
The Israeli operation took place near Beit Hanoun, an area often used by militants to fire rockets at Israel.
The clashes came after the Palestinian foreign ministry in Gaza City was bombed for the second time in a week.
Meanwhile, an Israeli soldier was killed and six were wounded in an ambush by Palestinian militants in the West Bank town of Nablus.
The al-Aqsa Martyrs' Brigade, linked to Palestinian leader Mahmoud Abbas's Fatah party, said it carried out the attack.
Return to north
Israel launched its offensive in Gaza three weeks ago after one of its soldiers was abducted.
The Israeli strike injured some residents near the building
Israel's declared goal is the return of Cpl Gilad Shalit and an end to cross-border rocket fire from Palestinian militants.
Its forces returned to the north of the territory on Sunday after a 10-day absence.
But rocket attacks have continued, with four people were injured in the Israeli town of Sderot.
Israeli planes fired missiles at the Palestinian foreign ministry building overnight on Monday.
The attack destroyed what was left of the building, which had already been badly damaged on Thursday.
No-one was inside at the time, but rescue workers say nine people in nearby houses were injured.
Israel said the ministry was targeted because it is run by a senior figure in the Hamas movement, Foreign Minister Mahmoud Zahhar, who it accused of planning terrorist attacks.
Mr Zahhar described the first attack on his ministry last Thursday as an Israeli crime.