Story Highlights• NEW: Death toll rises to 6 as Israel reacts to rocket attacks
• Airstrikes come as fighting between Fatah, Hamas continues
• Internal fighting has killed at least 40 Palestinians since Sunday
• Three rockets land in Sderot, Israel, one hitting a school
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GAZA CITY (CNN) -- Israeli airstrikes -- targeting Hamas in retaliation for dozens of Qassam rockets fired from Gaza into Israel in the past four days -- killed at least six Palestinians on Thursday, Palestinian security sources said.
The airstrikes angered Palestinian officials, who accused the Israelis of taking advantage of violence between the Hamas and Fatah factions. That violence continued Thursday despite a fourth attempt at a cease-fire Wednesday evening.
"Israel has decided to escalate this, and this could lead to disaster," Palestinian Information Minister Mustapha Barghouti said. "... We have no peace partner."
Three Qassam rockets fell Thursday morning in the Israeli town of Sderot. One struck a school and slightly wounded one person, Israeli officials said. (Watch Israelis leave on buses after attack )
Since Monday, as many as 80 rockets have been fired from Gaza into Israel, an Israel Defense Forces spokeswoman said. More than two dozen rockets rained down Wednesday, wounding at least 17 people, Israeli authorities said.
The Israelis said they targeted the compound of Hamas' executive force -- the movement's elite military wing -- in Gaza City, a car believed to be carrying Hamas operatives with weapons also in Gaza City, a Hamas post in northern Gaza City and a Hamas post in Rafah near the border with Egypt. (Watch Palestinian guards control traffic on a busy Gaza City street )
Israeli Foreign Minister Tzipi Livni warned Thursday that the Hamas actions would have consequences.
"A message should be conveyed to the Palestinians whereby terror has a price: The Palestinian government is the one responsible for the aggressive actions. It bears responsibility and they choose not to control it," she said.
Miri Eisen, spokeswoman for Israeli Prime Minister Ehud Olmert, said Israel had "had enough" of the cross-border violence.
"Israel will take every defensive measure to stop these rocket attacks," she said. "We will defend our citizens against the rockets, against the weapons, against the Iranian-backed Hamas who are attacking Israel."
An official from the Izzedine Al Qassam brigades, Hamas' military wing, said the Palestinian people have the right to defend themselves against "Israeli crimes" in any way they see fit, threatening possible suicide attacks.
An Israeli security source said Israeli forces have "more strategic targets" they can hit.
"We want to show the terrorists we know where they are," the source said.
In addition, the Israel Defense Force said it sent an additional small group of tanks to join the force already in place near the border of Gaza, and a very limited Israeli force was inside Gaza near the northern section of the border.
Meanwhile, internal Palestinian violence flared again Thursday during a funeral for some of the 19 Palestinians killed during Wednesday's violence. One person was killed when clashes broke out, Palestinian security forces said.
The clashes between Hamas and Fatah have killed more than 40 people since Sunday.
In Washington, U.S. Secretary of State Condoleezza Rice called Olmert and Palestinian President Mahmoud Abbas on Thursday to get their views on the latest violence, State Department spokesman Sean McCormack said.
"We want to see a reduction in the violence and restraint on both sides," McCormack said.
"We understand the Israeli government has a right to defend itself," he said. But, McCormack added, "We have also urged them to consider the consequences of their actions in defending themselves -- on Palestinian infrastructure, as well as on ... the prospects for moving forward the political process."
The Palestinian government is struggling to quell the latest round of fighting, which has highlighted the weaknesses of the Hamas-Fatah unity government formed earlier this year. Abbas canceled a planned trip to Gaza Thursday because of the violence, his office said.
CNN's Ben Wedeman, Nidal Rafa, Michal Zippori and Shira Medding contributed to this report.
Residents scurry through the streets of Gaza City after an Israeli airstrike kills one person.