The deployment also comes amid rising tension in Israel and the Palestinian territories after a Palestinian boy was kidnapped and killed, apparently in revenge for the murder of three Israeli teens in the West Bank.
"We are moving and we have moved forces in order to serve defence activities and forward preparation, but we have no interest in escalation," army spokesman Lieutenant Colonel Peter Lerner told journalists.
The reinforcements were reserve officers at "headquarter level, not in the field," Lerner said, and were purely a defensive measure.
"We have no interest in deepening the conflict with Gaza," he said.
More than 30 rockets were fired on Wednesday and Thursday from Gaza, which is controlled by Islamist movement Hamas, the army said.
Lerner said Hamas itself fired some of the rockets.
Israel responded with air strikes, wounding 11 Palestinians in the Strip.
Some rockets landed in southern Israel, causing damage to buildings but no casualties.
Hamas warned Israel it would "pay the price" for the abduction and killing of 16-year-old Mohammed Abu Khder in east Jerusalem on Wednesday.
The murder triggered an outpouring of rage in Shuafat, where Abu Khder's family lives.
Clashes erupted between stone-throwing Palestinians and Israeli riot police, raging from dawn on Wednesday until the early hours on Thursday, also spreading to many other areas in east Jerusalem.
Abu Khder's killing is believed to be a revenge attack for the kidnap and murder of Israeli teenagers Naftali Frenkel, Gilad Shaer and Eyal Yifrach in the West Bank in June.
Israel blamed Hamas for abducting and killing the three Israelis and waged a crushing arrest campaign against the movement's West Bank network, which resulted in the deaths of several Palestinians.
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