Mazlum-Der has also asked that the Israeli officials be detained if they enter Turkey, prosecutors said.
Turkish prosecutors are required to open an investigation whenever an official complaint is filed.
A spokesman for the Israeli Embassy in Ankara declined comment.
Turkey has long been Israel's closest ally in the Muslim world. But many Turks are furious about casualties among Palestinian civilians during the Gaza war that ended in a Jan. 18 cease-fire.
At the World Economic Forum in Davos, Switzerland, Prime Minister Recep Tayyip Erdogan scolded Peres over the Gaza war during a panel discussion and walked off a stage.
The offensive in Gaza left more than 1,300 Palestinians dead, many of them civilians. Thirteen Israelis were also killed.
Last month, a Spanish judge began an investigation into seven current or former Israeli officials over a 2002 bombing in Gaza that killed a top Hamas militant and 14 other people, including nine children.
The judge acted under a doctrine that allows prosecution in Spain, and other European countries, to reach far beyond national borders in cases of torture or war crimes.