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Israel also faced a second day of violent Palestinian protests in Jerusalem after the discovery of the body of a 16-year-old Palestinian boy on Wednesday in a forest near the city.
Israeli police are investigating the possibility that he was the victim of a revenge killing over the deaths of three Jewish teenagers, whose abduction on June 12 Israel has blamed on Islamist Hamas militants in the occupied West Bank.
Israeli Prime Minister Benjamin Netanyahu said if Gaza rocket fire stopped then Israel would also halt its actions.
But he added in a speech that if "firing toward our residents in the south continues, then our bolstered forces there will act forcefully".
Lieutenant-Colonel Peter Lerner, a military spokesman, said troops were taking up "defence positions" in Israeli communities that have been struck by the rockets from Gaza. He did not comment on the scale of the deployment.
It is the first time since the border began to heat up in mid-June - in tandem with an Israeli military sweep and search for the three abducted Israeli youths in the West Bank - that Israel has announced troop movements near the Gaza Strip.
"We are moving and we have moved forces," Lerner said in a conference call with foreign journalists. "Everything we are doing is to de-escalate the situation but on the other hand to be prepared if they don't de-escalate."
Israel has "no interest in deepening the conflict with Gaza - the absolute opposite is true", he added.
Abu Ubaida, spokesman for Hamas' armed wing, Izz el-Deen Al-Qassam Brigades, accused Israel of breaching a ceasefire brokered after a 2012 eight-day cross-border war, and said the group would respond according to developments on the ground.
"Our people know well how to exact a heavy price from the enemy," Ubaida said at a news conference in Gaza.
Netanyahu convened his security cabinet on Thursday for a fourth time since Monday, an official said, as tension remained high in Jerusalem in anticipation of the funeral of the Palestinian youth, Mohammed Abu Khudair.
Abu Khudair's body underwent an autopsy on Thursday and his burial was set for Friday, his family and a police spokesman said. The funeral is likely to stir strong emotions among Palestinians and could trigger further confrontation.
Police clashed with a few dozen stone-throwing Palestinians in Jerusalem's Arab neighbourhood Shuafat and a police spokesman said six people were arrested, but the violence was on a much smaller scale than on Wednesday.
The military said Palestinians in the Gaza Strip had fired more than 40 projectiles into Israel on Thursday and that rockets struck two homes in the southern town of Sderot, causing no casualties.
Israel launched air strikes against at least three Hamas training facilities in Gaza, residents said, adding that 15 people had been injured.
U.N. human rights chief Navi Pillay condemned both Israelis and Palestinians on Thursday for the latest flare-up of violence across the Gaza border and also Abu Khudair's killing.
"From a human rights point of view, I utterly condemn these rocket attacks and more especially I condemn Israel's excessive acts of retaliation," Pillay told journalists in Vienna.
The Palestinian youth Abu Khudair was last seen alive being bundled into a van on Wednesday near his home in the Arab neighbourhood of Shuafat in Jerusalem, a day after the burials of the Jewish teenagers, who were abducted on June 12.
"I unequivocally condemn the murder," Netanyahu said.
"The police investigation is ongoing. We don't know yet the motives or the identities of the perpetrators, but we will. We will bring to justice the criminals responsible for this despicable crime, whoever they may be."
Palestinian President Mahmoud Abbas, who accused Jewish settlers of killing the teenager, spoke by telephone with the youth's father on Thursday.
"Mohammed is one of the martyrs of this great people," Abbas said, according to the official Palestinian news agency, WAFA.
The killing of Abu Khudair also drew international condemnation and the United States urged Abbas's Palestinian Authority to "take all necessary steps to prevent an atmosphere of revenge and retribution".