* Israeli civilian shot while working on Gaza security fence
* Palestinian girl killed by shrapnel in Israeli air strike (Adds Hamas efforts to prevent escalation, U.N. comment, border crossing shut)
By Nidal al-Mughrabi
GAZA, Dec 24 (Reuters) - A Gaza sniper shot dead an Israeli civilian over the border on Tuesday and Israel hit back with air strikes on two Hamas training camps which hospital officials said killed a Palestinian girl near one of the targets.
The Israeli man, who the military said was working on Israel's security fence, was the first Israeli killed on the Gaza frontier in more than a year.
His death, which drew a swift threat of retaliation from Prime Minister Benjamin Netanyahu, came amid heightened tensions after two suspected Palestinian attacks - a bus bombing near Tel Aviv on Sunday that caused no casualties and the wounding of an Israeli policeman in a stabbing on Monday.
Officials from Hamas, the Islamic group which rules Gaza, and witnesses said Israeli aircraft bombed the group's training camps in Khan Younis and al-Bureij. Witnesses said Israeli tanks had fired shells east of Gaza city.
Gaza hospital officials said a three-year-old girl was killed by shrapnel during the Israeli strike on the Bureij facility. They had initially estimated her age at two years.
She was standing with other family members outside their home near the camp and two of her brothers were wounded, the officials said. In a statement, Hamas condemned the girl's death as "a criminal and cowardly act".
The Israeli military said in a statement its aircraft, tanks and infantry had taken part in a series of strikes.
"The sites targeted were 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," the military said.
Hamas Government spokesman Ehab Al-Ghsain said the group was "making internal efforts to contain the situation" and that it has contacted Egyptian mediators to prevent escalation.
Egypt last year brokered a ceasefire that ended an eight-day war between Israel and Hamas. U.N. Secretary-General Ban Ki-Moon called on the sides to abide by the 2012 truce and "exert maximum restraint to prevent another cycle of bloodshed."
Earlier a Palestinian was killed in a separate incident in northern Gaza, hospital officials said. An Israeli military spokeswoman said he was handling an explosive device near the security fence and that soldiers fired at him after warnings.
Israel shut the Kerem Shalom commercial crossing on the Gaza border, an Israeli defence official said.
There was no immediate claim of responsibility for the sniper attack, which followed a Palestinian rocket strike on southern Israel on Sunday that caused no casualties.
Commenting on the sniper attack, Netanyahu said: "This is an extremely grave incident and we will not ignore it. Our policy has been to thwart (Palestinian attacks) and to respond forcefully, and that is what we will do in this case."
However, since the November 2012 war, both Israel and Gaza's Hamas Islamist rulers have been wary of taking military action that could trigger widescale fighting.
No one was hurt in Sunday's bomb blast on the bus, which had been evacuated after the explosives were spotted, and the wounded policeman was expected to recover. But the incidents, blamed by Israel on militants, fuelled concerns of a new Palestinian uprising as peace talks show few signs of progress.
Hamas praised Sunday's bus bombing - the first in Israel in more than a year - but stopped short of claiming responsibility.
Violence in the West Bank has increased in recent months. At least 19 Palestinians and four Israelis have been killed in the occupied territory since the U.S.-brokered talks on Palestinian statehood resumed in July after a three-year break. (Writing by Maayan Lubell, Editing by Jeffrey Heller, Gareth Jones and David Evans)