JERUSALEM (CNN) -- Four Palestinian fighters were killed Thursday in clashes with Israeli soldiers, Palestinian medical sources said.
Israel Defense Forces earlier confirmed that Palestinian militants and Israeli troops traded fire in Gaza on Thursday, saying the soldiers hit at least two Palestinians.
Israeli troops have been carrying out operations in central Gaza to thwart militants who've been launching Qassam rockets into Israel and to combat Palestinians operating near the Israeli-Gaza border.
According to the IDF, three Qassam rockets were fired into Israel on Thursday, with one of the rockets falling near an elementary school.
Israel's recent military activities against Gaza-based militants may be having an impact. Hamas leader Ismail Haniyeh said Wednesday that he would be willing to negotiate a cease-fire deal with Israel.
Such a deal would call for Hamas to stop firing rockets into Israel and for an end to the Israeli military's targeted killings of Palestinian militants, Haniyeh said.
Haniyeh's remarks were made in a phone conversation with an Israeli television reporter and first reported Tuesday night. The overture follows a series of punishing Israeli attacks against Palestinian militants in the past two days, killing at least 11, including a senior leader of the radical Islamist group Islamic Jihad.
Israeli officials were dismissive of Haniyeh's comments.
Israeli Cabinet Minister Shaul Mofaz told Israeli radio that "mediation is something to think about, but one thing needs to be made clear: Till the firing stops, we must continue with the policy that we are taking in Gaza and not stop for even one hour."
Israeli President Shimon Peres called Haniyeh's comments a "pathetic attempt to move international attention from the crimes of the Hamas and the Islamic Jihad of shooting at innocent civilians," and said that if militants stopped firing rockets, then "Israel will immediately hold its fire so there is no need for negotiations."
Israel has refused to negotiate with Hamas, which took control of Gaza in June, until it agrees to submit to international benchmarks, including recognizing the state of Israel and renouncing violence.
Since June, Israel and the international community have put tough economic sanctions on Gaza, causing an increasingly dire humanitarian crisis in the coastal region of 1.5 million people.
According to the Israeli military, more than 3,600 rockets and mortars have been fired from Gaza into Israel since Israel pulled out its troops and settlements from Gaza in 2005. The military said the number of rocket attacks has more than doubled since Hamas took over control of Gaza in June.
The situation threatens to overshadow the peace process that was restarted after last month's talks in Annapolis, Maryland, where Israeli and Palestinian leaders pledged to negotiate a final-status agreement by the end of 2008. E-mail to a friend