However, the United States urged restraint on both sides, saying there was no military solution to the conflict.
Israel's Deputy Prime Minister Silvan Shalom warned of a new offensive on the coastal territory unless militant rocket attacks ceased.
"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," Shalom told public radio.
"We won't allow frightened children to again be raised in bomb shelters and so, in the end, it will force us to launch another military operation.
"I hope we can avoid it, but it is one of the options we have, and if we don't have a choice, we will use it in the near future," he said.
Three Palestinian children - aged two, four and 11 - were hit by flying glass in one of six overnight raids, said Moawiya Hassanein, head of the Palestinian emergency services in Gaza.
There were no other reports of casualties.
Hamas points fingers – West urges restraint
The head of the Islamist Hamas movement's government in the Gaza Strip, Ismail Haniya, blamed the Jewish state for the increase in tensions.
"We call on the international community to intervene to stop this escalation and Israeli aggression," he said in a statement.
In Washington, State Department spokesman Philip Crowley told reporters Israel has a right to self-defence. "At the same, as we've said many times, we don't ultimately think there is a military solution to this," he said.
"Our message remains to the Israelis and Palestinians that we need to get the proximity talks going, focus on the substance, move to direct negotiations and ultimately arrive at a settlement that ends the conflict once and for all."
Britain and France also expressed concern at the escalation, calling for restraint and the launch of US-backed indirect talks between Israel and the Palestinian Authority.
"We call on all parties to show restraint," a Foreign Office spokeswoman said in London. "We encourage Israelis and Palestinians to focus efforts on negotiation and to engage urgently in US-backed proximity talks."
In Paris, France's foreign ministry echoed British concern.
"Any initiative likely to raise tension is not appropriate, not welcome, not constructive," said ministry spokesman Bernard Valero, urging "all sides to act responsibly" and "take brave and necessary measures to restore trust."
Resurgence in violence
The air strikes came after a rocket fired by Palestinian militants landed near the southern Israeli city of Ashkelon late on Thursday, causing damage but no casualties, the military said.
Nearly 20 rockets have been fired into Israel in the past month, including one that killed a Thai farm worker, in the worst violence since the end of Israel's 22-day assault on Gaza that began in December 2008.
Since the war, which killed some 1,400 Palestinians and 13 Israelis, Israel has routinely responded to rocket fire by targeting smuggling tunnels and workshops it says are used to make rockets.
Three of the overnight Israeli strikes struck near Khan Yunis in southern Gaza. Two missiles hit a guard post of Hamas's armed wing, the Ezzedine Al-Qassam Brigades.
A fourth raid destroyed a workshop in Nusseirat refugee camp in central Gaza, Hamas and witnesses said. In the other raids, a small dairy was destroyed in western Gaza City.
The Israeli military said it hit "a weapons manufacturing site in the northern Gaza Strip, a weapons manufacturing site in the central Gaza Strip and two weapons storage facilities in the southern Gaza Strip."
"The (army) holds Hamas as solely responsible for maintaining peace and quiet in the Gaza Strip," it said.
Haniya said his government was in "contact with other Palestinian factions to maintain the internal consensus (truce), to protect our people and strengthen our unity."
The increased rocket attacks come amid tensions over Israel's settlement plans for annexed east Jerusalem that have stymied US efforts to launch peace talks and after fresh clashes along the Gaza-Israel border.
Two Israeli soldiers, including an officer, were killed along with two Palestinian gunmen on March 26-27 when Israeli tanks made a brief incursion into Gaza.
And on Tuesday, a Palestinian teenager was killed by Israeli troops near the border of the blockaded coastal strip.
