Under current Israeli law, an assailant must be a member of the "enemy forces" against Israel for the action to be considered terrorism, said Mayan Malkin, a spokeswoman with the Defence Ministry.
But in this case the shooter was Jewish and his attack cannot be designated as terror, said Malkin on Tuesday.
The four Arabs from the Israeli village of Shfaram were killed by a 19-year-old Israeli soldier, Eden Nathan Zaada.
Israel's army said the armed man was a deserter with professed anti-Arab views.
He belonged to the Kahane Kach organisation classified by both Israel and the US as a "terror movement".
Authorities later said he was trying to thwart Israel's evacuation of Jewish settlers from the Gaza Strip.
Prime Minister Ariel Sharon called the shooting "a despicable act by a bloodthirsty terrorist".
Jewish terror not covered
"The law doesn't cover Jewish terror," said Orna Kohn, a lawyer with the Adalah legal centre for minority rights in Israel.
"If this had been the same bus and same attack but committed by a Palestinian, then they would have been covered by the law"
lawyer, Adalah legal centre, Israel
"If this had been the same bus and same attack but committed by a Palestinian, then they would have been covered by the law."
Terror victims or their relatives are entitled to monthly compensation for the rest of their lives.
A committee lead by Defence Ministry officials decided to give the Shfaram victims a lumpsum amount rather than a lifelong monthly payment, a ministry statement said, without mentioning an amount.
But the committee did not agree to call them victims of a terrorist act. "It is not possible to recognise them as falling under this law," it said.