In a video released by the SITE Intelligence Group on jihadist forums and translated by the US monitoring service, Zawahiri also lashed out at US President Barack Obama, calling him a liar and demanding he admit defeat in Iraq, Afghanistan and North Africa.
Criticising the new Egyptian government – led by a president drawn from the Muslim Brotherhood – as corrupt, he said a battle is being waged in Egypt between a secular minority and Muslims seeking implementation of Sharia law.
The Egyptian doctor, the former deputy to slain al-Qaeda leader Osama bin Laden, said these Egyptians want to see their government liberated from US influence and Palestinian victory over Israel, SITE reported.
"The battle isn't over but it has started," Zawahiri said, urging "every sincere person in Egypt" to "wage a popular campaign to incite and preach in order to complete the revolution, which was aborted.
"The revolution in Egypt must continue and the Muslim Ummah must offer sacrifices until it achieves what it wants and until it snatches from the corrupt forces … the dignity and honour of Egypt."
Massive protests erupted on January 25, 2011 and toppled former Egyptian president Hosni Mubarak after more than 30 years of iron-fisted rule. He was replaced by the Islamist Mohamed Morsi after elections earlier this year.
Zawahiri said liberating Omar Abdul Rahman, an Egyptian cleric jailed in the US for his role in the 1993 World Trade Centre attack, and inmates at the US prison at Guantanamo Bay was an "obligatory duty for every Muslim".
"I call upon Muslims to capture citizens of the countries that wage wars against Muslims," he said.
"Our captives or Sheikh Omar Abdul Rahman will not be liberated except through force, for it is the only language that they understand."
In that vein, he made a reference to Warren Weinstein, a relief worker with USAID who was captured in Lahore, Pakistan in August 2011.
Zawahiri also called Obama a "professional liar".
"Obama must admit he and his allies are standing in the defeated line, and that Osama bin Laden, may Allah have mercy on him, and the rest of the Mujahedeen and the Muslim Ummah are standing in the victorious line, whether anyone likes it or not."
In a second, 58-minute video, also summarized and translated by SITE, Zawahiri called upon Egyptians to take part in protests "against the Israeli embassy and against normalisation and the peace treaty with Israel, and against the Israeli occupation of the land of Palestine, and against any concession and surrender to it, and against every siege in Gaza."
He also asked Morsi – whom he described as a president with no authority – specific questions, including what his positions were on "the jihad to liberate Palestine," as well as Sharia rule and Egypt's participation in the US "war on terror". – Sapa-AFP