Israeli media say troops have killed three Palestinian militants, in the bloodiest clash since a cease-fire between Israel and Hamas ended last week.
Reports say the militants were spotted Tuesday planting explosives near a security fence between Israel and the northern Gaza Strip. They were shot and killed in an exchange of fire.
There was no immediate Palestinian comment.
Earlier, militants fired several rockets into the western Negev desert in southern Israel. There were no reports of casualties or damage.
The rocket fire came after both sides observed a 24-hour period of calm that saw a drop in cross-border attacks from the Hamas-controlled Gaza Strip.
In spite of the violence, Israel said it will open three crossings with the Gaza Strip on Wednesday, to allow in shipments of humanitarian aid and commercial goods.
Separately on Tuesday, Hamas declared its willingness to extend the six-month cease-fire with Israel that ended on Friday.
Israel says its foreign minister, Tzipi Livni, will meet with Egyptian President Hosni Mubarak in Cairo Thursday for talks about a new truce in Gaza.
In Brussels, the European Commission pledged more than $17 million in food aid for people living in the Palestinian territories and Iraq. The pledge came in response to a U.N. appeal.
And Israel's top Roman Catholic cleric is calling on Hamas to settle its feud with rival movement Fatah. In a pre-Christmas message, Latin Patriarch Fouad Twal also spoke about what he called the injustice of the suffering in Gaza.
Israel has threatened a major military campaign in Gaza if the attacks into Israel from the territory continue, although both Hamas officials, including Mahmoud al-Zahar and Israeli defense authorities such as Deputy Defense Minister Matan Vilnai, say they want to avoid that.
Some information for this report was provided by AFP, AP and Reuters.