Children aged four, five and seven, and a 30-year-old religious education teacher, the father of two of the young victims, were shot dead on Monday as they arrived for classes at the Ozar Hatorah school in the southwestern city of Toulouse.
The killer, riding a powerful scooter, is suspected to be the same gunman who shot dead three soldiers of Arab origin in two incidents earlier this month in Toulouse and nearby Montauban.
“In France today there was a despicable murder of Jews, including small children,” Netanyahu told a meeting of his Likud party.
“It is too early to determine exactly what the background to the murderous act was, but we certainly cannot rule out the option that it was motivated by violent and murderous anti-Semitism.”
On the other side of the Middle East conflict, Palestinian negotiator Saeb Erakat also expressed his outrage, saying: “We strongly condemn all terrorist operations, and in particular the attack today in Toulouse.”
UN Secretary General Ban Ki-moon condemned the killings “in the strongest possible terms”.
Ban was “saddened by the tragic deaths” of the three children and the father of two of the dead children in the shooting in the southwest city of Toulouse, said UN spokesman Martin Nesirky.
President Nicolas Sarkozy suspended his re-election campaign until at least Wednesday, as police probed the third fatal shooting in the Toulouse area in eight days.
“In attacking children and a Jewish teacher, the anti-Semitic motive of the attack appears to be obvious,” Sarkozy said in a nationally televised address after he returned to Paris from the scene of the shooting.
In Washington, the White House condemned the “outrageous” and “unprovoked” shooting. “We were deeply saddened to learn of the horrific attack this morning,” said National Security Council spokesman Tommy Vietor.
New York police beefed up security around synagogues and Jewish institutions.
The dead teacher was named by a relative as Jonathan Sandler, originally from Jerusalem, who had moved to France last year. He had dual Franco-Israeli nationality.
European Commission president Jose Manuel Barroso said: “I strongly condemn this odious crime and express the horror that this blind violence inspires. Nothing is more intolerable than the murder of innocent children.”
The Vatican also voiced outrage, with spokesman Federico Lombardi condemning the “horrific and heinous act”, noting that it followed other “senseless violence” in France.
Australian Prime Minister Julia Gillard called the killings “an act of irredeemable evil”.
British Foreign Secretary William Hague spoke of an act of “calculated cruelty” which he said would “unite all decent people in revulsion and condemnation.”
Meanwhile Italian Prime Minister Mario Monti expressed “outrage and alarm,” stressing that “anti-Semitism, xenophobia and intolerance are utterly contrary to the… values that underlie all of humanity”.
His Spanish counterpart Mariano Rajoy said he was “shocked by the cruelty”, and his Belgian counterpart voiced his “horror and indignation”.
German Foreign Minister Guido Westerwelle was swift to stress that “anti-Semitism and violence against Jewish institutions or people of Jewish faith have no place in Europe and must be rigorously punished.”
Poland’s foreign ministry said: “Such acts of terror can have no justification and must be condemned unreservedly by the civilised world.”
Belgium, the Netherlands and Sweden also stepped up security around Jewish schools and other buildings, while European Jewish groups urged France to catch the gunman. There were expressions of outrage from Jewish groups on other continents.
“While many of the details are still emerging, it appears that this was a premeditated attack with the intention to murder Jewish children,” said Moshe Kantor, president of the European Jewish Congress.
Canadian Minister of Foreign Affairs John Baird sent a message on his Twitter account on Monday morning expressing his “solemn and sincere condolences to those affected by the shootings at Toulouse,” as Canada’s Jewish community said it shared “the terrible pain” being felt in Toulouse and beyond.