According to reports, six or seven militants broke through the Nahal Oz border crossing, attacking a fuel depot and killing two Israelis and injuring two more civilians before fleeing back to Gaza.
Islamic Jihad and the Popular Resistance Committees have claimed responsibility for the attack.
The militants were pursued by Israeli troops and at least three Palestinians were killed by tank fire, with another dying as the result of an air strike.
Earlier on Wednesday, Israeli troops killed one Hamas militant and wounded two others in a raid in south Gaza, which left two Israeli soldiers slightly wounded. The raid followed an operation by Israeli troops on Tuesday which left two Palestinians dead.
The fighting erupted just two days after Israeli Prime Minister Ehud Olmert and Palestinian President Mahmoud Abbas met in Jerusalem to discuss the peace process in their first meeting since a devastating Israeli incursion into the Gaza Strip killed some 120 Palestinians, including many civilians, in late February.
Israel said the February attack was in response to rocket attacks on Israeli border towns from Gaza. Abbas halted peace talks with Israel after the assault.
However, after meeting with U.S. Secretary of State Condoleezza Rice in Jordan on March 30-31, the Palestinian leader announced that he would resume talks with Israel.
