Gaza militants fired five Qassam rockets at the western Negev Wednesday evening. One rocket landed on a Sderot home wounding two people lightly.
Another rocket landed near a gas station in Kibbutz Nir'am and a third person was lightly wounded.
Eight people were treated for shock.
Earlier Wednesday, a Qassam rocket landed south of Ashkelon causing no injuries or damage. The Israel Defense Forces said that two rockets landed in Sderot Wednesday morning.
Militant group Islamic Jihad claimed responsibility for the rocket attacks in the morning prompting an Israel Air Force strike on its rocket launching sites in Gaza.
Meanwhile Wednesday, senior Hamas official Mahmoud Zahar said that his group wants to maintain calm in the Gaza Strip, but will not be the "protector" of the Israeli border with Gaza, threatening retaliation if attacked.
Last week, Hamas seized control of the coastal territory after five days of violent clashes with the rival Fatah party.
Zahar said the group is open to a cease-fire with Israel if the Israel Defense Forces halts its military operations in Gaza and the West Bank.
Zahar is a Hamas hard-liner with close ties to its military wing.
"Gaza is to some extent free. What will happen, we are going to help our people here and in the West Bank," he said, speaking in English.
Zahar, 62, has served as Palestinian foreign minister after Hamas was elected to power in early 2006, rejecting international calls for the movement to recognize Israel and renounce violence. Zahar was a vocal critic of Hamas' unity government with Fatah - which collapsed in last week's violence that left Hamas as the sole ruler of Gaza.
The infighting has left the Palestinians with two governments, a Fatah-led Cabinet in the West Bank that has been embraced by the international community and the Hamas rulers of Gaza, who have been widely shunned. Adding to the isolation, Israel has sealed Gaza's borders, raising concerns of a humanitarian crisis in the already impoverished area.
In the interview, Zahar said he was confident Israel will open the border to allow goods to travel in and out of Gaza. While he gave no indication that Hamas is ready to seek peace with Israel, he said the group would like to keep things quiet to, rebuild Gaza and resolve its differences with Fatah. "We are not enjoying ... [the] troubles with Fatah groups," he said. "We have to reconstruct our lives."
"If they are going to attack the Palestinian people in the West Bank or Gaza, the people are going to defend themselves, he said. Nobody will be a protector of the Israeli border ... We are not a protector of the Israelis. We are protecting our people. If they stop their aggression against the Palestinian people, the Palestinian people will not attack anybody," he added.
A surgeon who studied medicine in Egypt, Zahar was among the founders of Hamas in 1987 and remained close to the group's spiritual leader, Sheik Ahmed Yassin, until his assassination by Israel in 2004. Zahar himself survived an Israeli airstrike on his home in September 2003 that killed his oldest son and wounded his wife and a daughter.
While Hamas claims to have a collective leadership, members say privately that Zahar is leading the decision making.
Earlier Wednesday, an IDF soldier was moderately wounded and three Palestinian gunmen were killed as IDF troops entered the southern Gaza Strip, the IDF and militant groups said.
Two of the militants were named as 19-year-old Sulieman Hishan of the Popular Resistance Committees and 20-year-old Khaled al-Fara of Hamas. The third militant was also from Hamas.
At least seven other Palestinians were wounded in the shootout, according to Hamas, the Palestinian Resistance Committees and Islamic Jihad.
A short time later, the Israel Air Force launched an air strike targeting Palestinian rocket launch sites in the Gaza Strip, in the first air strike since Hamas seized control of the territory last week.
Troops acting undercover in the village of Karara were discovered by the gunmen who fired at them, prompting the army to send six tanks, 2 armored personnel carriers and a bulldozer to the area, Hamas and the Palestinian Resistance Committees said.
The army said the entrance of the troops had been planned, was not a broad operation, and was meant to counter militant activity, including arms smuggling.
In the West Bank Wednesday, two Palestinian militants were killed after an hour-long shootout with undercover police forces in Kafr Dan, a village near Jenin.
The militants were named as 33-year-old Ibrahim al-Abd of Fatah and 30-year-old Ziad Balayshe, a local Islamic Jihad commander.
Witnesses said the other militant was a local commander from a violent offshoot of Fatah. The radio reported, however, that he too was a member of Islamic Jihad.
30 jeeps and a bulldozer entered the village in an arrest raid, and a fierce exchange of fire ensued. The militants were killed and the house in which they were holed up was partly burnt, the witnesses said.
The army said armed men opened fire from the house on troops, who shot back, killing two militants.
