The BBC's Jon Donnison says the strikes were on a "relatively small scale"
Israeli planes have carried out 13 air strikes on the Hamas-ruled Gaza Strip, Palestinian sources have told the BBC.
Four of the strikes took place near the town of Khan Younis, where two Israeli soldiers were killed in clashes with Palestinian fighters last week.
Israel says the operation was targeting four weapons factories. Reports say three children were injured.
The latest violence is the most serious since the end of Israel's assault on Gaza in January 2009.
Palestinians and rights groups say more than 1,400 Gazans died in the conflict, while Israel puts the figure at 1,166. Thirteen Israelis, including three civilians, were killed.
Witnesses and Hamas officials said the latest Israeli raids targeted metal workshops, farms, a milk factory and small sites belonging to the military wing of Hamas.
The director of ambulance and emergency, Muawiya Hassanein, said that three children including an infant were slightly injured by flying debris.
Hamas Prime Minister Ismail Haniya has called on the international community to intervene in the latest cycle of violence between Gaza and Israel in order to avoid a possible escalation.
"We are contacting the other Palestinian factions in order to reach an internal consensus as to the measures we may take in order to protect our people and strengthen our unity," Mr Haniya said.
Israel says there have been at least 20 rocket or mortar attacks in the past month that have landed on its territory, one of which killed a farm worker.
The BBC's Jon Donnison, in Jerusalem, says Israel appears to be sending a signal that whenever there is militant activity inside Gaza it will respond.
Tim Franks, BBC News, Jerusalem
The air strikes were not a surprise. Israeli officials say there is an equivalence: if it is quiet within Israel's borders, then it will be quiet in Gaza.
Among Gaza's leaders there was a slight difference in emphasis. Ismail Haniya, the top Hamas man in the territory, condemned Israel's "escalation". But Ayman Taha, a spokesman, also said that Hamas was "working hard to deter any faction from acting individually".
So both sides are insisting that they want calm. But it is dangerous - and historically inaccurate - to imagine that violence can be neatly calibrated in and around Gaza.
In any case, the received wisdom among Gazans and Israelis is that another major clash is inevitable at some point: there are just too many sources of tension, too many triggers across the region.
It makes the job of pushing ahead with Israeli-Palestinian dialogue, and a wider resolution of the Arab-Israeli conflict all the more difficult, and all the more pressing.
In a statement released to the BBC, the Israeli military said Israel would "not tolerate terroristic activity inside Gaza that threatens Israeli citizens".
Deputy Prime Minister Silvan Shalom told public radio: "If this rocket fire against Israel does not stop, it seems we will have to raise the level of our activity and step up our actions against Hamas."
Correspondents say this kind of rhetoric has been heard in the past and should not be taken as a cue for imminent military action.
But tension is growing between Israel and Hamas, and some analysts view wider operations against Hamas as inevitable.
Palestinian news agencies reported that Israeli aircraft dropped leaflets over parts of Gaza on Thursday warning residents of retaliation for last Friday's killings of the soldiers in Khan Younis.
They were the first Israeli soldiers to be killed in hostile fire in Gaza in over a year. The military wing of Hamas claimed responsibility for those attacks.
Over roughly the same period, about 90 Palestinians in Gaza have been killed in a mixture of Israeli military operations and border clashes, according to the UN.
Hamas said police stations and training facilities were among the targets of Israel's overnight raids.
Khimar Abu Sada, professor of political science at al-Azhar university in Gaza City, told the BBC he had heard a number of explosions in the city.
"[On Thursday] the Israeli army distributed a number of leaflets in Gaza City warning the Palestinians to expect some kind of Israeli retaliation for the killing of two Israeli soldiers... so we were expecting something on Friday but not Thursday night," he said.
Tensions in the region are running high after a recent Israeli government announcement of plans to build 1,600 new homes for Jewish people in East Jerusalem, which the Palestinians want as a capital of a future state.
The US has criticised the Ramat Shlomo project, which prompted the Palestinians to pull out of US-brokered indirect peace talks.
The row has caused one of the worst crises in US-Israeli ties for decades, and the US is reportedly considering abstaining from a possible UN Security Council resolution against Israeli settlement expansion. The US usually blocks Security Council resolutions criticising Israel.
Militants in the Gaza Strip have recently stepped up rocket fire directed at Israel.
On Wednesday, they fired a rocket into an empty field in southern Israel, but there were no reports of casualties or damage, military sources said.
In December 2008, the Israeli armed forces launched a 22-day offensive in the Gaza Strip, bombing Palestinian cities before sending in ground troops - in response, Israel said, to Hamas rocket attacks on southern Israel.
After this, Hamas launched its rockets in increased numbers at Israeli towns near the Gaza Strip, before agreeing to a ceasefire.
Our correspondent says that Hamas has tried to rein in rocket fire from Gaza, and that there has been a reduction in attacks in the last year.
Israel would say that is a result of its military operations, our correspondent says.
But there are many militant groups in Gaza and Hamas does not control all of them, our correspondent adds.
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