The violence underscored deadlock in US-mediated talks between Israel and Palestinian President Mahmoud Abbas, whose peace strategy has been sapped by Hamas hostility along with continued Israeli settlement construction on occupied land.
The impasse had triggered sporadic rocket attacks this month from Gaza which drew Israeli airstrikes. On Friday, Palestinians ambushed soldiers who, the army said, had crossed the border to dismantle a mine. Two infantrymen were killed and two wounded.
The skirmish - in which the Israelis said they killed two Palestinian gunmen - was the fiercest since the three-week Gaza war of early 2009. Some 1,400 Palestinians, mainly civilians, and 13 Israelis, mainly troops, died in that conflict.
Hamas, having largely held fire since, announced that its men took part in the border clash, calling it self-defense. That drew veiled threats of escalation from Israel.
"We have been used to seeing breakaway (Palestinian) groups doing the firing, and Hamas trying to calm things down. Possibly it is loosening its grip, for all sorts of reasons," Defense Minister Ehud Barak told Israeli television on Friday.
"Should that indeed prove to be the case, then there will also be ramifications for Hamas," he said, but added: "We have no interest in returning the region to what was in the past." Israel captured Gaza, along with the West Bank and East Jerusalem, in a 1967 war. It withdrew unilaterally from Gaza in 2005 but has expanded Jewish settlements in the West Bank and East Jerusalem. Palestinians want a state in all the territories.
