Belgian police are investigating whether the killing of three people, including an Israeli couple, at the Jewish museum in Brussels on Saturday was a targeted assassination or a random antisemitic attack.

On Tuesday, federal authorities quickly denied media reports that a suspect had been arrested, and the Israelis – Emmanuel and Mira Riva, who were in their 50s – were buried in Tel Aviv. The Haaretz newspaper speculated that they may have been murdered because of connections to Israel's secret services.

The Rivas' teenage daughters and 200 other mourners at the ceremony listened as the Belgian ambassador to Israel, John Cornet d'Elzius, promised that every effort would be made to track down their killer. He said the Belgian government would "oppose antisemitism in our society" – apparently a response to critical comments made by the Israeli prime minister, Binyamin Netanyahu.

Belgian police were reported to be investigating all possible scenarios, including a "targeted assassination" as well as an act of antisemitism. The third fatality was a Frenchwoman, and a young Belgian man remains critically ill.

Experts in Israel and elsewhere have said the manner of the killings suggested planning and execution by a trained specialist. On Sunday, Belgian police released a 30-second video clip from the museum's security cameras showing a man wearing a dark cap, sunglasses and a blue jacket enter the building, take a Kalashnikov rifle out of a bag, and shoot into a room before calmly walking away.

Claude Moniquet, a Belgian counter-terrorism expert, told RTL that the perpetrator appeared to be a "cold killer, someone who had already seen death and already killed".

Israeli media reports said the Rivas were accountants formerly in government service. Emmanuel Riva worked for an official agency called Nativ, which dealt with the emigration of Jews from the former Soviet Union. Mira Riva was employed by the prime minister's office – often a euphemism for the Mossad and Shin Bet secret services. Both had been posted to Israel's embassy in Berlin.

Amir Oren, a military commentator for Haaretz, suggested the attack may have been an act of retaliation by agents of Iran or the Lebanese Shia movement Hezbollah.

But Moniquet questioned this scenario. "There are thousands of former members of the Israeli intelligence services, so if two of them are the object of a targeted operation, they must have had a particularly important role or done something that struck a particularly raw nerve in the Middle East," he said. "If that is the case, why kill them in the museum and not in their hotel, in a park … in a restaurant or on the street?"