Israel has bombed four Hamas training sites in Gaza, a day after Palestinian militants fired rockets into Israel.
The overnight air raids came hours after a Palestinian militant was killed and 10 others injured in clashes with the Israeli army near the border.
No casualties resulted from the air strikes or the rocket in Beersheva - the first attack on that city since Israel's 2009 Gaza offensive.
Israel says it holds Hamas responsible for all attacks emanating from Gaza.
Palestinian witnesses said the the fighting started on Wednesday after an Israeli tank entered northern Gaza. The Israeli army says it was trying to stop militants planting explosives along the fence.
Islamic Jihad said its militants opened fire on the tank, and that one man was killed and two wounded when the tanks returned fire.
The Ministry of Health in Gaza said three children were among those wounded by the shrapnel.
Doctors in Gaza said that in a separate incident, two Palestinian workers collecting rubble were injured after being shot by Israeli soldiers close to the border fence.
Later on Wednesday, a rocket fired from the Gaza Strip hit a house in the southern Israeli city of Beersheba, about 30 km (20 miles) from the Gaza Strip. No casualties were reported.
Officials said one house was extensively damaged when it was hit by a Grad rocket, which have a longer range than the homemade rockets which have been fired from Gaza before.
Residents took refuge in safe rooms prepared for such incidents before the rocket hit.
A second Grad rocket was reported to have fallen near the town of Netivot, causing no injuries.
Also overnight, the Abu Ali Mustafa brigades, the military wing of the Popular Front for the Liberation of Palestine, said fighters launched three mortar shells toward the Nahal Oz military base military, and another two toward Israeli infrastructure east of al-Zaitoun, the Maan news agency reported.
The Islamist group Hamas, which runs the Gaza Strip, and Israel have largely halted hostilities since the 2009 war in Gaza, but skirmishes often break out around the border area.
Although members of Hamas's military wing rarely carry out attacks, the Israeli military says it holds the group responsible for all militant activity in the Gaza Strip.