Tzipi Livni, the foreign minister, said on Tuesday Israel would stand by its new policy of firing artillery shells into Gaza in an effort to stop rocket fire at Israel.
"The role of the Israeli army is to defend Israeli civilians, combat terrorism and prevent rocket attacks," Livni told public radio. "As long as Palestinians fire at residential area, the army must reply."
An Israeli military spokesman echoed Livni's comments.
"There has been no change in policy," he said on customary condition of anonymity. "We will continue to fight them intensely, while trying to avoid hurting innocent civilians."
Hadil Ghabin, a nine-year-old Palestinian girl, was killed and 13 members of her family were wounded on Monday when an Israeli shell struck a house in the Bait Lahiya region of the northern Gaza Strip.
A seven-year-old boy was also killed in an air strike on Friday night.
On Tuesday Zeev Boim, the Israeli deputy defence minister, apologised for the girl's death but said military operations would continue as long as rockets continue to be fired at Israel.
"We are very sorry about it, but you have to understand that the military's task is to defend the security of the citizens of Israel," Boim said.
"If the Hamas government will not control these terrorists from firing Qassam [rockets] against Israeli civilians in cities and communities, we will continue to push these citizens out of the range of these rockets."
At Hadil's funeral on Tuesday, her mother said: "What did we ever do to them to deserve this? Please make them stop killing our children, please!"
Shells continued to fall in the area as mourners carried Hadil's body away.
Israel has stepped up its strikes against Palestinian rocket launchers since the new Hamas-led Palestinian government took power two weeks ago.
Islamic Jihad, which has been behind much of the rocket fire, said it would continue the attacks.
Laila El-Haddad in Gaza contributed to this article.