JERUSALEM (CNN) -- At least three Israeli missiles hit the Palestinian Interior Ministry in Gaza early Thursday, hours after Palestinian militants fired more than 40 Qassam rockets into southern Israel.
One of those rockets struck near a college, killing one person, according to the Israeli military and emergency medical services. The Palestinian rockets are a near daily occurrence but have only occasionally injured or killed people.
The strike at the ministry injured several people, according to Palestinian sources. Another rocket hit the building several minutes later, the sources said. A six-month-old child was struck by shrapnel and killed, the sources said.
The ministry strike was part of a series of Israeli airstrikes on Gaza in retaliation for the rocket attack. They included one outside Gaza City that killed two children, Palestinian medical sources said.
The Israeli military confirmed eight airstrikes in Gaza. The targets were rocket manufacturing and launching sites and a headquarters building, the Israelis said. Palestinian sources said two militants were killed.
The continuing violence came as an opinion poll in a leading Israeli paper suggested most Israelis think their government should negotiate with Hamas -- the militants in control of Gaza -- for a cease-fire and the release of a captured soldier.
The poll, conducted by the newspaper Haaretz and the polling company Dialog, found 64 percent of Israelis in favor of talks.
"It now appears that this opinion is gaining traction in the wider public, which until recently vehemently rejected such negotiations," according to the newspaper.
"According to the findings, Israelis are fed up with seven years of Qassam rockets falling on Sderot and the communities near Gaza, as well as the fact that [Gilad] Shalit has been held captive for more than a year and a half," the newspaper said.
Shalit was 19 when he was captured June 25, 2006, by Palestinian militants who tunneled into Israel and attacked an army outpost near the Gaza-Israel-Egypt border.
Apart from the one death and one injury Wednesday by Palestinian rockets that hit Sapir College, near Sderot, no other injuries were reported from the rockets.
Another Israeli airstrike -- targeting a rocket cell in northern Gaza -- killed one civilian and injured three others just outside Jebalya, Palestinian medical and security sources said.
Five Hamas members were killed in an earlier airstrike in Gaza, the sources said.
The Israeli military confirmed it carried out the airstrikes in northern Gaza, but offered no details.
Earlier this month, Israeli Prime Minister Ehud Olmert resisted pressure to launch a broader military operation against Palestinian militants in Gaza after a rocket attack seriously wounded an 8-year-old boy in Sderot. The boy's leg was amputated.
Instead, Israel retaliated with troops carrying out airstrikes in Gaza against Hamas targets.
Olmert has vowed not to "slacken" against the ongoing attacks on Israel, which he described as an "almost daily war."
"We will continue to struggle in order to reduce to nil the threat that is upsetting the quality of life of residents of the south," he said.
As part of that struggle, Olmert said, Israel will continue its military operations and its blockade of "materials that could serve the terrorist organizations, including energy."
Israel has allowed some fuel and medical supplies into Gaza, but has kept the border crossings closed except to meet emergency humanitarian needs. The block on food, fuel and medicine has led to long lines at stores and left hospitals without heat.
Human rights groups have protested against the blockade, accusing Israel of collectively punishing civilians along with the territory's Hamas leadership.
On Monday, thousands of people formed a human chain along Gaza's roads in a Hamas-led protest over the blockade. Hamas does not recognize Israel's right to exist, and Israel and the United States consider it a terrorist organization.
"This may not always be loved but it is an important part of counterterrorist activity," Olmert said.
He also said the Israeli government is building 13 new schools in Sderot and surrounding areas that will be reinforced to protect them from the salvo of rockets.
It is part of a $14 million plan approved by the Knesset in January.
The poll figures were obtained in a Haaretz-Dialog poll conducted Tuesday under the supervision of Professor Camil Fuchs of Tel Aviv University. E-mail to a friend