An Israeli air strike killed a young Palestinian girl in the Hamas-controlled Gaza Strip on Thursday after an Israeli died in a militant cross-border mortar attack on a kibbutz.

Palestinian medics said a girl of about eight was killed and two women were injured outside their house near Khan Younis in the southern Gaza Strip. The army said it carried out an air strike in the area, saying it was targeting a militant.

The attack in Gaza came after Palestinian militants shelled an Israeli kibbutz, killing one person and wounding three.

Hamas's armed wing said it fired three mortar bombs which it said "killed a Zionist and wounded some others". Israeli police described the attack as a rocket strike on a factory at the Nir Oz kibbutz in southern Israel.

Both sides vowed to keep fighting.

"We will confront the occupier with all our means and we will continue striking the Zionist military sites and settlements around Gaza in response to the continued aggression against our people," Hamas said in a statement.

Israeli government spokesman David Baker said Hamas would be held accountable for salvoes into Israel. "Israel cannot and will not allow the situation to continue," Baker said.

Prime Minister Ehud Olmert, enmeshed in a corruption scandal that could force him to step down, has faced mounting public pressure to launch a large-scale military operation in the Gaza Strip to stop rocket and mortar attacks. Olmert has denied wrongdoing but said he will quit if indicted.

Palestinian militants in Gaza regularly launch cross-border rocket attacks at Israel which sow panic in border towns. Two Israelis were killed in similar attacks last month.

Israel has tightened its blockade on the Gaza Strip, which Hamas seized after routing President Mahmoud Abbas's Fatah faction a year ago, and often conducts raids into the territory which it says are aimed at ending the attacks.

Violence along the Gaza border has marred peace talks between Olmert and Abbas, who holds sway in the West Bank. Egypt has so far failed in its efforts to broker a truce to curb rocket attacks on Israel and Israeli raids in the Gaza Strip.