Belgian police are hunting for an assailant who shot dead three people at the Jewish Museum in Brussels.
French authorities have tightened security at Jewish sites following another attack that prompted fears of arise in anti-Semitism.
Belgian authorities said a French woman and an Israeli couple died and a Belgian man was seriously injured after being shot in the face and neck.
A spokeswoman for the Brussels prosecutor's office Ine Van Wymersch said: "From the images we have seen, we can deduce that the author probably acted alone and was well prepared,"
"It's still too early to confirm whether it's a terrorist or an anti-Semitic attack, all lines of investigation are still open," she said.
Security around all Jewish institutions in Belgium was raised to the highest level.
About half of the country's 42,000-strong Jewish community lives in Brussels.
The French government tightened security around synagogues and Jewish cultural centres yesterday following an attack on two Jews in suburban Paris hours after the Brussels shootings.
French President Francois Hollande said police would catch those responsible for the attack yesterday evening on two young men wearing traditional Jewish clothing as they were leaving a synagogue in Creteil.
Both men were in hospital after being beaten by two men, one on bicycle and one on foot, Agence France-Presse reported.
"We must do everything to fight against anti-Semitism andracism," Hollande told news channel I-Tele today.
French Interior Minister Bernard Cazeneuve said in a statement that he had instructed police to "immediately secure sites linked to the Jewish religion or Jewish culture".
At some 550,000, France's Jewish community is the largest in Europe, though violence such as the 2012 murders of three Jewish children and a rabbi by Islamist gunman Mohammed Merah have prompted higher emigration to Israel or elsewhere.
France's Agence Juive, which tracks Jewish emigration, says 1,407 Jews left France for Israel in the first three months of this year, putting 2014 on track to mark the biggest exodus of French Jews to Israel since the country was founded in 1948.
Last year's total of 3,300 was a 73% increase on 2012.
Israeli Prime Minister Benjamin Netanyahu, in a statement from his office, strongly condemned the Brussels killings. They were, he said, "the result of endless incitement against the Jews and their state".