Israel said in response it would deal first diplomatically with the deed, emphasizing to the U.N. and international aid organizations that Hamas was responsible for the cross-border raid.
After that, Deputy Israeli Defense Minister Matan Vilnai said, "We will choose the time and place to respond."
Two of the four terrorists who crossed over into Israel were shot and killed by the IDF at a filling depot near the Karni border terminal with the other two fleeing back to Gaza, the Jerusalem Post said.
Military aircraft soon swooped over the area and bombed a car on the Palestinian side of the border, killing two more terrorists allegedly involved in the attack.
Palestinians said at least four more people, including children, were killed by the bombings.
Israel was expected to resume the fuel supply in a few days.
"We have an obligation to prevent a humanitarian disaster in Gaza," Vilnai said.