A video later distributed by the Qassam Brigade showed the four attackers reading statements, but the image of a fourth man who survived the raid was blacked out, suggesting he could still at large.
Border crossings have become a frequent recent target for militant raids, signaling a possible tactical shift.
On April 9, gunmen killed two Israeli civilian workers at the Nahal Oz fuel transfer terminal, which supplies fuel to Gaza.
On Thursday, a Palestinian sniper fired on Israeli soldiers near Nahal Oz, and two gunmen were wounded trying to infiltrate Kerem Shalom.
Leibovich said that Thursday's much smaller attack at Kerem Shalom might have been a scouting mission to measure Israeli response time at the crossing.
Israeli officials accuse Hamas of cynically exploiting the deprivation of Gaza residents.
"They know when we target a crossing, we have no choice but to close it. They're looking for a way to stop the flow of supplies to civilians," Leibovich said. "They ride on the backs of the civilians all the time."
The emphasis on targeting crossing points also might be motivated by a standing desire by Gaza militant groups to kidnap Israeli soldiers as bargaining chips. In a similar raid near Kerem Shalom in June 2006, attackers captured Israeli army Cpl. Gilad Shalit, who remains captive somewhere in Gaza.
The armored vehicle used in yesterday's attack was one of the dozens supplied by the international community and used by security forces of the Fatah party. Hamas inherited the equipment when it vanquished Fatah forces last summer, but it's unclear how many working armored vehicles the group possesses.
Four other Palestinians, three of them Qassam cadres, died in Israeli airstrikes yesterday, bringing the death toll to seven, the group said.
Rushdi Abu Alouf and Ashraf Khalil write for the Los Angeles Times.
