The two Israeli officials said the co-pilot was believed to have stabbed the captain before cabin crew entered the cockpit and took control of the plane.
An Israeli official had earlier told Reuters the plane transmitted the emergency signals after the pilots got into a physical altercation with each other.
About the time the plane landed in Saudi Arabia on Wednesday, Doron Spielman, a spokesman for the Israeli prime minister's office, told Reuters the incident was not believed to have been a hijacking, describing it as a "different incident".
The two officials, speaking on the condition of anonymity to brief reporters, said Israel's assessment was that the incident was an attempted "terror attack" and not related to any kind of mental health issue with either of the pilots.
In a video purportedly of an Israeli passenger on board the FlyDubai flight and carried widely by Israeli media, the passenger said one of pilots was seriously injured and the other was slightly injured, after one of the pilots was stabbed.
Saudi Arabia's Tabuk airport, where the plane eventually landed safely, said both pilots had been hospitalised after suffering injuries.
Neither the airport or the purported Israeli passenger identified the attacker.
Flight FZ1073 from Dubai to Tel Aviv diverted to Saudi Arabia as it flew over Jordanian airspace, transmitting a general emergency signal and then another emergency signal that indicated possible unlawful interference, according to flight-tracking website Flightradar24.
The Boeing 737 plane, which Israeli media said had about 150 Israeli passengers on board, then again transmitted the initial general emergency signal before later landing at Tabuk airport in northwestern Saudi Arabia, the website said.
The aircraft's data appeared to show that it had suddenly and rapidly descended by almost 4270 metres in less than 30 seconds before the first emergency signal, Flightradar24 said.
Israeli media published conflicting reports on the incident, with some outlets reporting that a pilot had tried to crash the passenger plane in an alleged attempted suicide attempt.
Some Israeli media outlets identified the pilots as Omani and Emirati nationals, while others said they were Russian and Ukrainian.
The incident triggered a national security consultations in Israel, which has no official diplomatic relations with Saudi Arabia, where the plane landed.
In a statement, the Israeli prime minister's office said the situation was "under control" and all measures were being taken to bring the Israeli passengers back to Israel.
Prime Minister Benjamin Netanyahu, who earlier held security consultations on the incident, had cleared his schedule for the rest of the day to manage the crisis, an Israeli official said.
Netanyahu on Sunday met UAE President Sheikh Mohamed bin Zayed Al Nahyan during a a rare visit to the Gulf country.
Israel and the UAE have forged close security, military and economic ties since establishing diplomatic ties in 2020.
The UAE is yet to comment on the incident, while the Dubai-owned airline has only said that the flight experienced an "incident" and diverted to Tabuk, where it landed safely, and that all passengers were safe and accounted for.
Yasmin Abukasis said her daughter Miriam, who was among the passengers on the flight, had told her that she had heard screaming and that a man holding a knife had forced one of the pilots onto the floor, and that there was blood everywhere.
Israeli media published a photo purportedly taken from inside the plane, which appeared to show a passenger's blood-soaked shirt.
FlyDubai operates daily return flights between Dubai and Tel Aviv, a route that is popular among Israeli tourists.
