A number of al-Qaida-inspired groups have carried out rocket attacks from Gaza and Egypt's Sinai Peninsula, as well as shootings in the West Bank. Israeli intelligence calls these groups part of a "global jihad" movement.
Aviv Oreg, a former head of the Israeli military intelligence unit that tracks al-Qaida, said the plot marked the first time it has been directly linked to an attempted attack in Israel.
"This is the first time that Ayman al-Zawahri was directly involved," he said. "For them, it would have been a great achievement."
The Shin Bet said the three suspects made contact with al-Qaida over the Internet. It said they planned on traveling to Syria — where various jihadist groups are battling the forces of President Bashar Assad — for training.
Oreg said that many foreign fighters fighting the Assad regime are from Chechnya and predominantly Muslim parts of Russia and speculated that the militants with the phony documents would be from there.
Al-Zawahri's location is unknown, but he was last believed to be in Pakistan. He is the subject of an intense manhunt and is not believed to personally go online or pick up the phone to discuss terror plots, experts say.
Last year, a threat that began with a message from the Yemen-based al-Qaida in the Arabian Peninsula to al-Zawahri led to the closures of embassies across the Middle East and Africa, a U.S. official said at the time. The message essentially sought out al-Zawahri's blessing to launch attacks.
Al-Qaida-inspired groups are on the rise in the Gaza Strip, which is run by the Islamic militant Hamas.
These groups accuse Hamas of being too lenient because it has observed cease-fires with Israel and has stopped short of imposing Islamic religious law, or Shariah, in Gaza.