Three Hamas members were killed by Israeli forces on Tuesday
Palestinian medical workers say a young girl has been killed by Israeli tank fire in the Gaza Strip.
They say the girl's body was recovered from a house that was hit by a tank shell near Khan Younis.
A spokesman for the Israeli military said a ground force had attacked militants in the area attempting to fire rockets into Israel.
Israel's security cabinet said it would support Egyptian-brokered efforts to reach a truce with Gaza's Hamas rulers.
The meeting of senior Israeli officials with security responsibilities was expected to discuss a possible invasion of Gaza to prevent militant attacks on southern Israel.
Palestinian medical officials said six-year-old Hadeel Smari was decapitated by the tank shell explosion while she was in the back yard of her house.
Two adult relatives were wounded in the attack, doctors said. Israeli officials said they were unaware of any civilian casualties.
Hamas said one of its gunmen was killed during the Israeli operation in the area.
A mortar shell later hit an Israeli paint factory near Gaza, slightly injuring two people.
On Tuesday Hamas said three of its members were killed by Israeli fire after launching rockets.
Correspondents say there has been public pressure on Israel's leaders to counter militant fire with more than the pinpoint tactics currently in use.
"The security cabinet decided this morning to support Egyptian efforts to achieve calm in the south and to end the daily targeting of Israeli civilians by the terrorists in Gaza," said Israeli Prime Minister Ehud Olmert's spokesman Mark Regev.
"In parallel, the security cabinet has instructed the military to continue its preparations in the unfortunate event that the Egyptian track should prove unsuccessful," he added.
Four Israeli civilians have been killed by Palestinian rockets or mortars this year.
About 500 people, nearly all of them Palestinians killed in Israeli raids and more than half of those armed militants, have died in violence since the troubled Israeli-Palestinian peace process was revived in November 2007.
Israel has sealed off the Gaza Strip and blocks all but essential humanitarian supplies, while launching regular raids in an attempt to counter militant fire.