In a 15-minute recording posted on Islamist websites on Saturday, Zawahri also criticized Islamists who had formed political parties in Egypt and supported the Egyptian military in ousting former Egyptian President Mohammed Morsi.
"I give this piece of advice to whoever supported Morsi and I tell them first we have to admit that legitimacy doesn't lie in elections and democracy but it lies in Sharia," Zawahri said.
"Sharia is not electing Morsi president of a republic, a president of a secular and nationalistic state," he added.
The recording, posted two days after U.S. Secretary of State John Kerry gave his seal of approval to Egypt's new leaders saying that they had restored democracy, also lashed out against U.S. policy and the Egyptian army.
"The crusaders, the secularists, the pro-U.S. army and former Mubarak supporters and a few of those who are linked to the Islamists have worked with Gulf money and U.S. planning to overthrow Morsi's government," Zawahri said.
More than 300 people have been killed in Egypt since the army removed Morsi and his Muslim Brotherhood from power on July 3 in response to mass protests against his rule.
The popular mood in Egypt had swung against the Brotherhood after Morsi was accused of trying to establish himself as a new dictator during his first year in office.
Pro-Morsi supporters have been staging two main sit-ins in Cairo since his ouster asking to bring him back to power.
"What has happened is the greatest evidence that taking democracy as a path to Islamic rule has failed," Zawahri said.
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