In a 15-minute audio message posted online late today, Ayman al-Zawahri also lashed out at the Egyptian military, the country's secular and liberal elites as well as the Coptic Christian minority, accusing them of conspiring against Morsi solely because he was an Islamist.
Egypt's army ousted Morsi, the country's first democratically elected leader, on July 3 after days of mass protests demanding the president's removal.
"We have to admit first that legitimacy does not mean elections and democracy, but legitimacy is the Shariah (Islamic law)... Which is above all the constitutions and laws," al-Zawahri said in comments addressed to Morsi's supporters.
He condemned the Brotherhood for having "tried its best to satisfy America and the secularists" by relinquishing "jihad," usually invoked by al-Qaida to mean armed struggle.
Also Read
He also noted that Morsi's government was overthrown despite its acceptance of Egypt's landmark peace treaty with Israel and security agreements with the United States both of which Islamic militants sharply oppose.
Al-Qaida and other Islamic extremists roundly reject democracy as a Western-imposed system, and oppose it on the grounds that it puts man's laws above those of God.
Turning to Egypt's military, al-Zawahri, who is Egyptian and grew up in a Cairo suburb, accused the army of being a pawn of US interests.
"The Americanised army, was raised by America's aid, training courses and exercises and their allegiance was bought to fulfil the Americans' orders and protect US interests as well as maintain the security of its foster child, Israel," he said.
The message's authenticity could not be independently confirmed but was posted on a militant website commonly used by al-Qaida. It was produced by the group's arm, As Sahab.