The soldier, who has not been identified, went missing early Sunday after an anti-tank rocket hit an Israeli armoured vehicle, killing seven other troops, media reported.
The Al Qassam Brigades, the armed wing of the Palestinian Islamic movement Hamas, which rules Gaza, Sunday had announced the capture of an Israeli soldier.
The abduction took place after Israeli ground troops last week entered Gaza, following days of heavy air and naval artillery bombardments on the Palestinian enclave within Operation Protective Edge, which failed to stop rocket attacks on Israel.
At least seven Palestinians, including five members of a family, died Tuesday in bombardments in the centre and south of Gaza, bringing the death toll in the offensive to 584 Palestinians, mostly civilians, and the number of injured to 3,640, said Gaza emergency spokesperson Ashraf al-Qedra.
The UN said 100,000 people had been displaced in Gaza as they fled the conflict, and many had sought refuge at 69 school-shelters run by the organisation.
The movements of the population are restricted by the Israeli ground and naval blockade on the enclave and the closure of the Rafah crossing with Egypt, the only exit.
At least 29 Israelis have died during the offensive, 27 of them troopers who perished in the fighting and two civilians killed by rockets fired from Gaza on Israel.
Meanwhile, diplomatic efforts continued Tuesday in an attempt to put an end to the bloodshed, with US Secretary of State John Kerry and UN Secretary General Ban Ki-moon in Cairo to back an Egyptian ceasefire initiative and pressure the Palestinian side to accept it.
The ceasefire was rejected last week by Hamas, who termed it "humiliating" and demanded an end to the blockade and the release of Palestinian prisoners.
Gaza witnessed one of the deadliest assaults Sunday when the IDF raided the eastern Shejaiya neighbourhood, leaving around 100 Palestinians dead and hundreds wounded.