Suspect hunted in museum shooting
The attack, which came on the eve of national and European Parliament elections, led officials to immediately raise anti-terror measures and increase protection for Jewish sites.
Video of the attack showed a man calmly walking into the Jewish Museum, getting out a Kalashnikov shoulder rifle and starting to shoot before briskly walking away.
No one has claimed responsibility for the killings.
"We call on the whole population to help identify this person," deputy prosecutor Ine Van Wymersch said on Sunday.
She said the gunman who killed an Israeli tourist couple, a French woman and a Belgian man with shots to the face and throat "probably acted alone, was armed and well prepared."
The fourth victim died on Sunday afternoon, said a government official.
Officials said the shooter parked a car in the Sablon area of antique dealers, cafes and art galleries. The museum said in a statement the gunman came in, started shooting at the tourist couple at the entry "and then went on to the reception, where he shot the attendant."
Police detained one suspect late on Saturday but he was soon released and is now considered a witness.
Ms Van Wymersch said "all options are still open" regarding a motive for the shooting spree but the government has said it had the hallmarks of an anti-Semitic attack.
As in Belgium, Interior Minister Bernard Caseneuve ordered police around France to increase security at Jewish houses of worship and other Jewish establishments.
Israeli prime minister Benjamin Netanyahu blamed the shooting on European incitement against Israel and criticised what he called "weak condemnation" of anti-Semitic acts.
"There are those in Europe that are quick to condemn every building of an apartment in Jerusalem, but do not rush to condemn, or condemn with weak condemnations, the murder of Jews here or in Europe itself," Mr Netanyahu said at the opening of his weekly Cabinet meeting.
Belgian prime minister Elio Di Rupo swiftly condemned the attack and said Belgium stands united with its Jewish community of 40,000.
He also called Mr Netanyahu early on Sunday "to express the deep solidarity of Belgium with the Israeli population."