The police and security services have so far failed to locate the perpetrators of the arson attack on the Dawabsheh family in the West Bank village of Douma last month.
Two family members - 18-month-old toddler Ali and his father, Saed - died, and the child's mother and brother were seriously wounded.
The Shin Bet believes the attackers were part of a group of Jewish extremists calling themselves The Revolt, which is dedicated to fomenting violence between Israelis and Palestinians and ultimately bringing down the democratic Israeli government and replacing it with a Jewish kingdom.
Three suspects who were arrested last week were put under six-month administrative detention orders . One of them, Meir Ettinger, is believed to be the group's leader. However no proof has yet been established of a direct link between them and the arson attack.
Another group of minors who were arrested last weekend at a nearby settlement were released a day later after questioning.
Meanwhile, Yishai Schliessel, the perpetrator of the stabbing of Gay Pride paraders in Jerusalem a fortnight ago, has been ordered to undergo a second round of psychiatric evaluation as it remains unclear whether he is fit to stand trial.
At his remand hearing, Schliessel refused representation and would not address the court, saying only: "You have no authority to judge by the Holy Torah, therefore I am not interested in taking part in this illegal show, not myself and not through representation."
An internal investigation into why Jerusalem police failed to act over warnings that Schliessel, who was released less than two months ago after serving a prison sentence for a similar stabbing attack on the Gay Pride parade in 2005, could act again.
The two incidents sparked another round of bitter recriminations within Israeli society.
President Reuven Rivlin wrote in a message released in both Hebrew and Arabic after the murders: "From my people, there are those who have chosen the path of terrorism, and have lost their humanity."
He has received much public support for the remarks, but also online abuse and death threats.
Settler leader Daniella Weiss responded dismissively that "Rivlin can sleep quietly. He's not important enough to be killed."
A strictly Orthodox school in Jerusalem cancelled a planned visit by the president following his support of LGBT rights.
Writing on Facebook, former Shin Bet chief Yuval Diskin accused both the religious community and the settlers of fostering the murderers. He wrote that the authorities had allowed the creation of a parallel "state of Judea" and that "anyone who thinks that it's only a few dozen hallucinating youngsters is making a big mistake".
He claimed there was a much larger movement among the settlers that was prepared to support terror acts against Palestinians, and "under some scenarios, when they believe the 'sanctity of the land' is under threat, also against Jews".
