"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."
About 1,400 Palestinians were killed when Israel launched its last offensive on the Gaza Strip in December 2008.
Ten Israeli soldiers and three civilians also died over the 22-day period of the assault.
"Twenty rockets in the space of one month might not sound a huge amount compared to the intensive rocket fire preceeding and during the Gaza war of just over a year ago," Al Jazeera's Jacky Rowland, reporting from Jerusalem, said.
"Nevertheless, in comparison to recent months it did mark an escalation."
There was no claim of responsibility for Thursday's lone rocket, which caused no casualties.
The Israeli military said Friday's air raids had targeted weapons manufacturing and storage facilities in the central Gaza Strip, in Gaza City in the north and the southern part of the Palestinian enclave, all in response to rockets fired from the territory.
"The IDF [Israeli military] will not tolerate any attempt to harm the citizens of the State of Israel and will continue to operate firmly against anyone who uses terror against it," the Israeli army said in a statement.
"The IDF holds Hamas as solely responsible for maintaining peace and quiet in the Gaza Strip."
But witnesses and Hamas officials said that Israeli missiles hit two caravans near the town of Khan Younis and a cheese factory, while helicopters attacked a metal foundry in the Nusseirat refugee camp.
The children injured in the air raids were hit by flying glass, Palestinian medics said.
Fawzi Barhoum, a Hamas spokesman, told Al Jazeera that Hamas held the Israeli government led by Binyamin Netanyahu responsible for the "escalation", but said air raids had been expected because of threats by Ehud Barak, the defence minister, and other ministers.
He also blamed "the international community and the Arabs" for failing "to do anything about the situation in Gaza".
"The absence of the international community and the Arabs has allowed the Israelis to escalate the situation," he said.
There have been increasing tensions between Palestinians and Israeli security forces in the Gaza Strip, the West Bank and occupied East Jerusalem in recent weeks.
On Tuesday, a Palestinian teenager was killed and several others wounded as Israeli troops fired on protesters near the border between Gaza and Israel and last weekend two Israeli soldiers and two Palestinian fighters died during clashes.
Clashes have also broken out in the West Bank and Jerusalem over Israeli settlement plans, the reconsecration of a synagogue in East Jerusalem and other issues.