Israel is known for going to great lengths to recover the remains of fallen soldiers, both because Jewish law requires the body to be buried intact and because the army fears militants will try to use the remains as bargaining chips.
Israel has carried out a number of lopsided deals, most recently in January, exchanging hundreds of Arab prisoners for the remains of dead soldiers.
Tuesday's fighting began as a routine Israeli operation to uncover and destroy weapons workshops, but changed direction when the explosives-laden armored vehicle ran over an improvised bomb.
Masked Palestinian gunmen rushed to collect the body parts following the explosion, saying they would use the flesh to barter with Israel for the release of prisoners.
Israel rejected the demand outright.
Palestinian Cabinet minister Saeb Erekat said the Palestinian Authority "is exerting every possible effort" to return the body parts to Israel.
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