A Palestinian man grieves outside a hospital in Rafa, Gaza, on Saturday.

Story highlights

NEW: Over 20 mortars and rockets are fired into Israel from Gaza, Israel's military says

NEW: A 55-year-old man is killed in these attacks, an Israeli emergency spokesman says

2 Islamic Jihad commanders were among 7 killed in an Israeli strike, a group spokesman says

The Israeli military says it targeted a terror group, but does not specify which one

Gaza City CNN  — 

At least 10 people are dead in Gaza and southern Israel, in a wave of back-and-forth attacks between the Israeli military and Palestinian militants, according to medical and military officials.

The violence began when two Islamic Jihad commanders were among seven militants killed Saturday by Israeli strikes targeting a training camp in Rafah, Gaza, a spokesman for the militant group and medical sources reported.

The Israel Defense Forces said that more than 20 mortars and rockets were subsequently fired into their territory. A 55-year-old man was killed in the rocket attacks and 20 others were injured, according to Zaki Heler, an emergency services spokesman in Israel.

Palestinian medical sources told CNN that two people were killed in a second wave of Israeli airstrikes, launched in response to these rocket attacks.

According to Abu Ahmed, a spokesman for the Islamic Jihad, the original Israeli strikes occurred during a graduation ceremony. Two other members of his organization were injured in that attack, he said. Witnesses reported that at least 10 other people were wounded.

Afterward, Ahmed promised a “response … inside Israel very soon.”

Israeli police spokesman Micky Rosenfeld said that one of the rockets then fired from Gaza into southern Israel struck a building in Ashdod. An Israeli man in Gan Yavne was slightly injured by shrapnel.

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 IDF said in a statement that its forces continued to respond to threats from the Gaza Strip on Saturday night, targeting armed rocket launching tripods and people preparing to launch rockets into Israel.

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.

CNN’s Kevin Flower and journalist Talal Abu-Rahmi contributed to this report.