"I believe it is time to examine defining groups like La Familia and Lehava as terror groups, and I know the issue is being presented to security forces," Gantz said during a faction meeting of his Blue and White party.
Thousands of flag-waving Israelis on Sunday marched through Jerusalem's Old City during a nationalist procession marking Israel's 1967 capture of east Jerusalem.
Some marchers chanted "death to Arabs", as a number of Palestinians hurled projectiles from the rooftops.
Prime Minister Naftali Bennett ordered police to show "zero tolerance" towards Jewish extremists who planned to "incite" tensions, singling out La Familia.
Foreign Minister Yair Lapid described Lehava and La Familia as a "disgrace" who weren't "worthy of holding the Israeli flag".
La Familia is a group of fans of the Beitar Jerusalem football club, notorious for their anti-Arab racism and violence.
Lehava is an extremist right-wing group that fights against fraternisation between Jews and non-Jews which could lead to intermarriage. It is affiliated with the teachings of the late Rabbi Meir Kahana, whose Kach group is outlawed in Israel.
Not the first time
To designate an organisation as a terrorist group, one of Israel's security organisations -- the Shin Bet internal security agency, police, army or Mossad -- must issue a request to the defence ministry and receive the consent of the attorney general.
Following the defence minister's approval, the group will receive a three-month temporary designation, during which it can appeal the decision to the ministry as well as a special judiciary panel.
