Call for arrest
"There is prima facie evidence ... which indicates that South African citizens and/or residents are implicated in the commission of these crimes," the South African Press Association reported, citing a statement from the groups.
The two groups also called for the immediate arrest of Lieutenant-Colonel David Benjamin, a South African-born Israeli soldier, who was visiting the country last week to attend a conference.
Jewish community leaders in South Africa have criticised the probe call, calling it a "witch hunt".
The Israeli government has defended its military's conduct during the war as "necessary and proportionate" and has consistently said its troops respected international law.
In a report released late last month, Israel's foreign ministry said Israel had "a right and an obligation" to take military action to stop rocket attacks from Hamas in Gaza.
But it has said it is investigating about 100 complaints of misconduct by its forces during the war.
The 163-page report was published ahead of a UN war crimes investigation in the wake of accusations from human rights groups that Israeli forces committed war crimes and violated international law during the war.
Palestinian officials say 1,417 Palestinians, including 926 civilians, were killed during the fighting.
Israel says that the number killed was considerably lower, and that only 295 of the dead were civilians.
Ten Israeli soldiers were killed in the fighting, while three Israeli civilians were killed in rocket attacks.