* Three killed in museum attack, fourth seriously injured
* Anti-Semitism not ruled out as a motive
* France tightens security after Paris assault (Updates with condition of fourth victim, Netanyahu statement)
By Robert-Jan Bartunek
BRUSSELS, May 25 (Reuters) - Belgian police on Sunday were hunting a gunman who shot dead two Israelis and a French woman at the Jewish Museum in Brussels, in an attack French President Francois Hollande said was without doubt motivated by anti-Semitism.
Security around all Jewish institutions in Belgium was raised to the highest level following Saturday's shooting, while French authorities stepped up security after two Jews were attacked near a Paris synagogue.
Belgian officials released a 30-second video clip from the museum's security cameras showing a man wearing a dark cap and a blue jacket enter the building, take a Kalashnikov rifle out of a bag, and shoot into a room, before walking out.
"From the images we have seen, we can deduce that the perpetrator probably acted alone and was well prepared," said Ine Van Wymersch, a spokeswoman for the Brussels prosecutor's office.
"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 told a news conference.
Officials appealed for witnesses to the attack in the busy tourist district which is filled with restaurants and antique shops. The entrance to the Jewish Museum was lined with flowers and candles, and will remain closed to the public on Monday.
"The anti-Semitic nature of the act - a shooting, with intent to kill, in the Jewish Museum of Brussels - cannot be denied," said Hollande, speaking about the Brussels attack.
"We must do everything to fight against anti-Semitism and racism," he told news channel I-Tele on Sunday.
Hours after the Brussels shootings, two Jews were attacked and beaten in Paris as they left a synagogue in the suburb of Creteil wearing traditional Jewish clothing.
POPE CONDEMNS 'SAVAGE ATTACK'
The two Israelis, Emmanuel and Miriam Riva, both in their 50s, were described by friends as former Israeli civil servants who were in Belgium on vacation.
A Belgian man who was also injured in the shooting remained in critical condition in hospital, authorities said.
Belgian Prime Minister Elio Di Rupo spoke by telephone with Hollande and Israeli Prime Minister Benjamin Netanyahu and held talks with the Jewish community in Belgium.
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". He offered Israeli cooperation in the Belgian investigation.
An Israeli official said Emmanuel Riva had formerly worked for Nativ, a government agency that played a covert role in fostering Jewish immigration from the former Soviet Union.
Along with the Mossad and Shin Bet intelligence services, the agency was under the authority of the prime minister's office.
Miriam Riva also formerly worked for the prime minister's office, the official said without elaborating.
Friends of the couple interviewed by Israeli media said they both worked as accountants in government service.
Pope Francis, in Tel Aviv on Sunday, condemned the attack in Brussels, where about half of Belgium's 42,000-strong Jewish community lives.
"With a deeply saddened heart, I think of all of those who lost their lives in yesterday's savage attack in Brussels," he said.
"In renewing my deep sorrow for this criminal act of anti-Semitic hatred, I commend to our merciful God the victims and pray for the healing of those wounded."
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 Mohamed 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. (Additional reporting by Maayan Lubell and Dan Williams in Jerusalem, Leila Abboud in Paris, Justyna Pawlak and Philip Blenkinsop in Brussels; Writing by Justyna Pawlak; Editing by Lynne O'Donnell, Sophie Hares and Eric Walsh)