Belgian police were yesterday hunting for an assailant who shot dead three people at the Jewish Museum in Brussels, and French authorities tightened security at Jewish sites following another attack that prompted fears of a rise in anti-Semitism.

Belgian authorities said a French woman and an Israeli couple died and a Belgian man was seriously wounded on Saturday after being shot in the face and neck.

"From the images we have seen we can deduce that the author probably acted alone and was well prepared," Ine Van Wymersch, a spokeswoman for the Brussels prosecutor's office told reporters.

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"It's still too early to confirm whether it's a ­terrorist or an anti-Semitic attack." 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 on Sunday 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 on Saturday 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.