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Two other members of the organization were injured, medical sources said.
"Our response will be inside Israel very soon," said Abu Ahmed, a spokesman for the militant group.
After Israeli forces struck the training camp Saturday, militants fired three rockets from Gaza into southern Israel, according to Israeli police spokesman Micky Rosenfeld.
One struck a building in Ashdod, he said. An Israeli man in Gan Yavne was slightly injured by shrapnel.
A graduation ceremony was taking place at the time of the original Israeli strikes, Ahmed said. At least 10 other people were wounded in the attack, witnesses said.
An Israel Defense Forces spokesman said it targeted a terrorist group in southern Gaza that was preparing to fire long-range rockets into Israel. The spokesman would not name the group, but said it was part of a larger organization.
The Israeli airstrikes targeted the same group responsible for recent rocket attacks on the Israeli port city of Ashdod, according to the Israeli military spokesman.
