Al Jazeera's Jacky Rowland, speaking from Gaza, reported that the attack on the interior ministry was one of three simultaneous missile attacks on Gaza.
"We're now learning there were three air strikes," she said.
"It seems Israel is trying to target what it is identifying as some kind of security infrastructure of the Hama authorities. The irony is that in most cases, these are not buildings that are actually being used by Hamas forces."
The recent air attacks bring the number of Israeli air raids on Friday to four.
"It seems to the people of Gaza that Israel is carrying out more or less indiscriminate attacks from the air and from the ground," Rowland reported.
"The biggest air strike - the one against the interior ministry building - has, as far as we can tell, largely claimed civilian victims."
The attack came a day after Ehud Barak, the Israeli defence minister, ordered the closure of all crossings into the Gaza Strip.
The closure is set to cut off the flow of vital supplies into the Palestinian enclave, which has been run by Hamas since the group seized control in June last year.
"This measure, which will remain in effect for several days, covers both commercial traffic and persons," an Israeli official said.
Shlomo Dror, a defence ministry spokesman, said the decision is meant to pressure the Hamas to halt rocket fire at southern Israel.
"It's time that Hamas decide to either fight or take care of its population. It's unacceptable that people in Sderot are living in fear every day and people in the Gaza Strip are living life as usual."
Israel kept all crossings into Gaza closed on Friday morning, meaning that about 20 trucks of food scheduled to pass during the day would not be allowed through, Dror said.
The UN agency in charge of Palestinian refugees, UNRWA, condemned the Israeli move.
"This can only lead to the deterioration of an already dire situation," said Christopher Gunness, an UNRWA spokesman, said.
The closure "can only lead to the further radicalisation of a depressed and demoralised people".
At the same, Israel is pushing ahead with its military offensive against fighters in both Gaza and the West Bank.
On Thursday, Ehud Olmert, the Israeli prime minister, said in a statement that his country was at "war" against fighters in the Gaza Strip.
The Israeli military has particularly intensified its operations in Gaza, with at least 32 people killed during the past week. In response, Hamas has begun firing rockets at Israel for the first time in months.
Some 150 rockets and mortars have struck since Tuesday, the Israeli army said.