The soldiers have posted photographs of themselves, on private online accounts, holding signs in Hebrew reading: "The nation demands revenge," or similar slogans.
The comments refer to three Israeli teenagers -- Gilad Shaar, Eyal Yifrach and Naftali Frenkel -- in the West Bank whose abduction incited a massive search across Israel. Their bodies were found, after a two-week hunt, earlier this week and laid to rest Tuesday.
Military commanders have been instructed to seek and punish those posting the photographs.
The Israel Defense Force Spokesman Unit, in a statement, referred to the call for revenge as a "severe incident," adding, "We regret that national feelings of sadness are being exploited by political elements for incitement, and the linking of those who serve in the IDF to this phenomenon."