Gaza City, Gaza (CNN) -- Israeli airstrikes and tank shells pounded parts of Gaza Tuesday -- killing a 4-year-old girl, Palestinian security and medical sources said -- after Israel said a Gaza sniper killed a Muslim Israeli man near a border fence.
The events began when a sniper in Gaza shot a Bedouin Israeli citizen -- Salah Shukri Abu Latyef, 22 -- who was performing maintenance work Tuesday on the fence separating Israel from the Palestinian territory's northern border, the Israeli military said.
Abu Latyef was from Rahat, a southern Israeli city inhabited mainly by Bedouins, an Arab Muslim minority in Israel, the military said.
Israeli Prime Minister Benjamin Netanyahu's office promised a forceful response, saying the shooting was a "very severe incident, and we will not let it go unanswered."
"Our policy until now has been to act beforehand and to respond in force, and this is how we will act regarding this incident as well," Netanyahu's office said.
Israeli warplanes launched strikes on and near some Gaza camps of the al Qassam Brigades -- the military wing of Hamas, which controls Gaza -- Hamas security sources said.
The Israeli military confirmed it launched tank and air attacks, saying it struck a weapon manufacturing facility and "a terror infrastructure in the southern Gaza Strip, a terror site and another terror infrastructure in the central Gaza Strip, and a concealed rocket launcher in the northern Gaza Strip."
One airstrike struck a house near an al Qassam camp in central Gaza, killing a 4-year-old girl and injuring three of her relatives, the Hamas sources said.
Israeli airstrikes also hit an empty field at an al Qassam camp near the southern Gaza area of Rafah, and an empty al Qassam training camp in the southern Gaza community of Khan Younes, the Hamas sources said.
Hamas said the training camps were evacuated after the Israeli's killing.
Israeli tank shells also hit near the al Maghazi refugee camp in central Gaza, according to the Hamas sources.
The sources said 11 people were injured in the airstrikes and tank attacks, in addition to the child who was killed.
The al Qassam Brigades claimed on its Twitter account that the slain Israeli was a soldier. The Israeli military, however, said Abu Latyef was a civilian.
The Israeli defense minister, Moshe Ya'alon, said Israel holds Hamas responsible for the shooting.
"We will not allow life in the south to be disturbed, and we will react in the sternest and gravest way to any attack on our sovereignty and injuries of our civilians and soldiers," Ya'alon said in a statement released by the defense ministry.
U.N. Secretary-General Ban Ki-moon is concerned about the violence, condemns Abu Latyef's killing and deplores the death of the Gaza girl and other Palestinian civilian casualties, his spokesman said Tuesday.
The Israeli military said Abu Latyef was the first Israeli civilian killed near the Gaza Strip since it launched a series of attacks there last year.
In Israel's "Pillar of Defense" operation in November 2012, the country's military launched strikes on Gaza designed to stop constant rocket fire. Eight days of round-the-clock warfare followed between Israel and Hamas. More than 160 Palestinians, many of whom were civilians, were killed. Six Israelis died, including civilians and soldiers.
Journalist Talal Abu Rahma reported from Gaza City; CNN's Michael Schwartz reported from Bethlehem in the West Bank. CNN's Saad Abedine, Hamdi Alkhshali, Kareem Khadder and Jason Hanna contributed to this report.