Said Phashpashe, an Israeli construction worker involved in building the fence, was killed and another person seriously injured when a roadside bomb detonated, the Israeli military said.
The suspected bomb carriers were on the Egyptian side of the border when an Israeli military force from Golani arrived. In the ensuing gunbattle, a bomb carried by one the attackers exploded, killing two of the suspects, The Jerusalem Post reported Monday.
The incident occurred early Monday near the Israeli community of Kadosh Barnea, about 30 kilometers (18.6 miles) from the Gaza Strip.
The attackers crossed into Israel and fired on Israeli vehicles with light weapons and a rocket-propelled grenade, killing the construction worker and seriously injuring the second victim, the army said. Soldiers from the Golani Brigade exchanged gunfire with the attackers, killing two of them.
Defense Minister Ehud Barak said the attack showed security is deteriorating on the Egyptian side of the border, Israel Radio reported.
"Egypt must take responsibility for its international obligations including the peace treaty with Israel and the security situation in the Sinai," the Hebrew language daily Maariv quoted Barak as saying.
Israeli communities near where the attack occurred were placed on alert and residents were instructed to remain in their homes as troops searched for other possible suspects, army spokesman Yoav Mordechai told Army Radio.
Netanyahu said the border fence was "meant to both prevent terrorism and the entrance of infiltrators. Its construction is of supreme national interest," he said, adding if its construction had not begun two years ago, Israel would be facing a flood of terrorists.
The border fence now covers 180 kilometers (112) miles. It is to be 240 kilometers (149 miles) long when completed. About 1,500 workers are involved in the construction.