One of the targets of Israeli raids was a factory in Gaza City
Leaders of the Hamas militant movement which controls the Gaza Strip have said they are working to curb rocket attacks against Israel by smaller factions.
Spokesman Ayman Taha said the Hamas government was trying to maintain calm in Gaza for "the national interest".
He spoke hours after Israeli planes carried out bombing raids on what it said were weapons factories in Gaza.
Hamas PM Ismail Haniya also urged the international community to intervene to avoid an escalation in violence.
"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.
Four of the strikes took place near the town of Khan Younis, where two Israeli soldiers and two Palestinian fighters were killed in clashes last week. Three children were reportedly injured in the Israeli strikes.
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.
Militants in the Gaza Strip have recently stepped up rocket fire directed at Israel.
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.
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.
Mr Taha told the BBC on Friday: "The government in Gaza is in charge of the situation, and it does know clearly who launches rockets.
"It is working hard to deter any faction from acting individually."
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 the 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.
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.
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.
The BBC's Jon Donnison in Jerusalem says that Hamas has tried to rein in rocket fire from Gaza, and that there has been a reduction in attacks in the past year.
Israel would say that is a result of its military operations, our correspondent says.
There are many militant groups in Gaza and Hamas does not control all of them, our correspondent adds.