The air strikes came after Israel threatened to respond to missiles being fired into Sderot.
Afterwards, the Izz al-Din al-Qassam Brigades warned it may renew its suicide bombing campaign.
Abu Ubaida, the group's spokesman, said: "This is an open war launched against Hamas. All options are open, including martyrdom operations."
At least two Israelis in the town of Sderot were injured by rockets fired by Palestinian groups on Thursday.
Miri Eisen, spokeswoman for the Israeli prime minister, told Al Jazeera: "Israel has been under attack for days, for weeks. The Hamas themselves have already openly said that they support terror.
"Israel restrained itself completely for the last five months when every day there were rocket attacks. Israel will defend our citizens, we will not let the Hamas, we will not let the rocket people, the launchers, this Hamas-led government define the situation."
Israel says that about 70 Qassam rockets have been fired into the southern Israeli town in the past two days.
Tanks and armoured vehicles also moved into the Gaza Strip on Thursday in what an Israeli army spokesman described as a "defensive operation".
David Chater, Al Jazeera's correspondent in Jerusalem, said: "The Israeli prime minister is under great pressure to try and stop these rocket barrages ... and Israel has obviously decided to loosen its policy of restraint.
"[The Executive Force] are not completely, exclusively Hamas and also they have not been responsible, as far as we know, for launching any Qassam rockets, that has been in the hands of the military wing of Hamas and Islamic Jihad.
"So we don't yet know the reasons why the Israelis decided to hit the Executive Force compound."
Mustafa al-Barghouti, the Palestinian information minister, said that the air strikes showed that Israel is "no peace partner".
"The Israeli reaction is a recipe for disaster," he said.
"If they want to get rid completely of rocket attacks they know the way, it is very simple, we have offered them a complete, comprehensive and reciprocal ceasefire. They are the ones that rejected that."
|An injured woman is rescued |
from the damaged buildings
The attack came shortly after Mahmoud Abbas, the Palestinian president, cancelled a visit to Gaza for talks on the ceasefire between Fatah and Hamas in the territory.
Abbas had been due to travel to Gaza to meet Ismail Haniya, the Palestinian prime minister.
Meanwhile, a truce agreed between the two factions - their fourth in as many days - was generally holding despite some sporadic violence.
At least one Palestinian was killed and 11 injured in factional fighting in Rafah, and Fatah said at least five of its men were also abducted by its rival group.
Hamas said a member had been critically wounded in an early morning shooting.
Three previous ceasefires collapsed within hours since violence first flared on Sunday.
At least 43 people, the vast majority of them Fatah loyalists, have been killed since Sunday. The toll has included two civilians, with more than 100 people wounded.