Israel confirmed that its warplanes attacked a building housing the Palestinian interior ministry headquarters causing substantial damage. Earlier a training camp in Rafah used by Hamas was bombarded during an air raid.
The raids follow comments from Israel's prime minister who said Hamas had escalated the conflict with Palestinian militants by firing a rocket that struck a school in the Israeli city of Ashkelon.
No one was wounded in the attack but Prime Minister Ehud Olmert said it was an escalation of "unprecedented gravity".
"This strike on the heart of Ashkelon is a very serious incident which constitutes an escalation of unprecedented gravity in the campaign of terror waged by Hamas, which leads the Palestinian Authority," Mr Olmert said.
The armed wing of Hamas, the Ezzedine al-Qassam Brigades, claimed responsibility for firing the rocket in response to what it called "Israeli aggression".
"We will teach the occupation a lesson they will never forget,” the militant group said in a statement.
The attack came just hours after an ultimatum set by Palestinian militants for the release of Palestinian prisoners in exchange for abducted Israeli soldier Gilad Shalit.
Mr Olmert again ruled out any negotiations with militants and promised to strike anyone linked to them, in a thinly veiled reference to Syria.
Israel said it believed Shalit, who is wounded and has been seen by a Palestinian doctor, was still alive. He was seized nine days ago in a Palestinian raid
"We will hit all terrorists. No one who attempts to harm the state of Israel will be spared," he said, implicitly blaming Syria.
Israel accuses Syria of harbouring militants including Hamas' political leader Khaled Meshaal.
Israel has sent tanks and troops back into the Gaza Strip for the first time since leaving last September after a 38-year occupation in a bid to free its soldier.
Extended range
The Qassam rocket landed on a school in the center of Ashkelon south of Tel Aviv. No one was inside the school at the time of the attack.
"This rocket had two engines which extended its range from 9.5 kilometres to 12 kilometres," an Israeli spokeswoman said.
It is the first time a Qassam rocket has landed in central Ashkelon, raising concerns that the militants are in the process of upgrading their missile technology.
The homemade devices are notoriously inaccurate and generally have a maximum range of around 12 kilometres.
Rockets fired previously at Ashkelon have tended to land in an industrial sector south of the center.
Israeli television reported that the rocket had been fired from a building near the Erez border crossing between northern Gaza and Israel.
But an Israeli army spokeswoman said the rocket originated from a point further to the west.
The television report quoted anonymous Israeli officials as saying that the development could lead to a ground operation in northern Gaza by Israeli forces.