The move came moments before the latest truce - brokered by Egyptian mediators late on Monday - came into force at 08:00 local time (05:00 GMT) Tuesday.
Gaza officials say the four-week conflict has killed nearly 1,900 Palestinians. Some 67 Israelis have also died so far.
"The Israel forces will be redeployed in defensive positions outside the Gaza Strip and we will maintain those defensive positions," Israeli military spokesman Lt-Col Peter Lerner said.
Shortly before the ceasefire came into effect Israeli warplanes staged at least five airstrikes in Gaza prompting a barrage of retaliatory rocket fires from the Palestinian resistance groups the skies fell silent.
There have been several truces called during the conflict but few have lasted. The new agreement proposes that delegations from all sides should attend further talks in Cairo.
The main Palestinian demands remain on the table, notably a full Israeli troop withdrawal from Gaza, the end of the blockade of the territory and the opening of border crossings.
UN Secretary General Ban Ki-moon has welcomed the ceasefire, and he called on both sides to hold talks in Egypt to begin as soon as possible.
Images of the bloodshed have triggered tensions across the region and earned the Tel Aviv regime increasingly harsh criticism for the high number of civilian casualties.
Israel and Hamas separately confirmed that they would abide by the new 72-hour ceasefire which emerged from two days of Egyptian and US mediated talks in Cairo.
The truce announcement came after international outrage grew over an Israeli strike near a UN school on Sunday that killed 10 people, denounced by the UN as "a moral outrage and a criminal act", with the United States saying it was "appalled".
The Israeli army began its military offensive on July 8, and nine days later sent in ground troops to tighten the siege on Gaza.
NGD/BA