Late on Friday aircraft shot at least four missiles at buildings used by Hamas security forces in Gaza City, wounding eight, several of them seriously, said Muawiya Hassanein, the head of Gaza emergency services.
The site used to house the offices of Palestinian president Mahmud Abbas before his Western-backed Fatah party was ousted from Gaza by the Islamist Hamas in 2007.
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Warplanes also hit smuggling tunnels on the border with Egypt and another site in central Gaza, without causing casualties, witnesses said.
Fearing further strikes Hamas ordered the evacuation of all its security offices, a security source said.
The Israeli military had no immediate comment on the strikes, but Israel routinely responds after rocket attacks from Gaza.
The airstrikes came after a rocket fired by Gaza militants on Friday slammed into the southern Israeli city of Ashkelon, causing no casualties but some damage, and prompting sharp criticism from the United Nations.
The 122 mm Katyusha-type rocket landed next to a high-rise apartment building, damaging parked cars and shattering building windows, the Israeli military said.
The United Nations condemned the attack, saying that "indiscriminate rocket fire against civilians is completely unacceptable and constitutes a terrorist attack".
Sirens gave the 125,000 residents a few minutes warning before the rocket hit a residential area.
The port city was frequently targeted by rocket fire from the Hamas-run Gaza Strip before Israel launched its devastating three-week offensive on the Palestinian territory in December 2008.
Just over 100 rockets and mortar shells have been fired from Gaza at southern Israel so far this year, compared with a daily barrage before the war, but most have not had the capacity to reach Ashkelon, 10 kilometres north of Gaza.
"We call on the de-facto authorities in Gaza to ensure that these kinds of actions do not occur," a spokesman for Middle East peace envoy Robert Serry said.
"Violent actions must not be allowed to undermine progress in the ongoing talks between Israel and the Palestinians," he said.
Israeli Prime Minister Benjamin Netanyahu for his part said that "Israel takes the firing on Ashkelon very seriously," according to his office.
