Israel accused Lula of trivializing the Holocaust and says it is fighting to destroy Hamas and return hostages taken by the militant group on October 07.
The main Jewish organization in Brazil also criticized Lula's comments.
Speaking from an African Union summit in Ethiopia, Lula said, "What is happening in the Gaza Strip with the Palestinian people has no parallel in other historical moments. In fact, it did exist when Hitler decided to kill the Jews”.
But he has since been vocally critical of Israel's retaliatory military campaign, which the Hamas-run health ministry in Gaza says has killed more than 28,800 people, mainly women and children.
His latest comments come after Israel's Prime Minister Benjamin Netanyahu vowed to press ahead with an offensive in Rafah - the southern-most Gazan city where some 1.5 million people have fled - in the face of increasing international pressure.
Netanyahu said Lula's remarks amounted to "Holocaust trivialization and an attempt to harm the Jewish people and the right of Israel to defend itself".
"The comparison between Israel to the Holocaust of the Nazis and Hitler is crossing a red line," he said in a statement.
Six million Jewish people were systematically murdered by Hitler's Nazi regime during the 1930s and 1940s.
Israel has summoned the Brazilian ambassador for a meeting on Monday.
The Brazilian Israelite Confederation said Lula's remarks were a perverse distortion of reality which offends the memory of Holocaust victims and their descendants".
Lula endorsed South Africa's case of genocide brought against Israel at the International Court of Justice (ICJ) last year.
Judges at the ICJ ruled in January that South Africa's case against Israel could proceed.
The court instructed Israel to prevent its military from committing acts which might be considered genocidal, to prevent and punish incitement to genocide, and to enable humanitarian assistance to the people of Gaza.
Brazil and South Africa are members of the BRICS group of countries - an alliance of some of the world's most important developing economies brought together to challenge wealthier Western nations.
On the ground in Gaza, the World Health Organization has said the territory's Nasser hospital has ceased to function following an Israeli raid. The IDF said its operation was precise and limited and accused Hamas of cynically using hospitals for terror.
Meanwhile, efforts to broker a ceasefire between Israel and Hamas have been taking place in Cairo, though Qatar mediators said recent progress was not very promising.
