The military said that "two terrorists who infiltrated into Israel hurled explosive devices" at soldiers. The soldiers returned fire, killing them.
About a half hour earlier, two Palestinians damaged the security fence and tried to cross into Israel. Troops opened fire, killing one, the military said. The other was detained for questioning, it said.
In a third incident, soldiers spotted two Palestinians trying to breach the border. They were arrested and found to have knives and wire cutters on their persons, the military said.
There was no immediate comment from Hamas in Gaza.
Also today, the Israeli Army claimed that most of the deaths of Palestinians during the Gaza unrest have been unintentional.
An unidentified senior officer in Israel's southern command told Haaretz that snipers had been aiming at protesters' legs, but people had been killed after bending down, when struck by a ricocheting bullet or when a sniper missed the target.
Israel has been accused by the United Nations, European Union and rights groups of using excessive force against unarmed protesters.
Hamas says the protests are aimed at breaking a crippling border blockade that was imposed by Israel and Egypt after the Islamic militant group overran Gaza in 2007.
The protests also press for a "return" of Palestinian refugees and their descendants to what is now Israel. Hundreds of thousands of Palestinians fled or were displaced in the 1948 war over Israel's creation.
- AP, AAP