Urging Hamas to reject previous deals made between the Palestinian Authority (PA) and Israel, Ayman al-Zawahiri said such deals were "surrender accords".
"Your only alternative is to pursue the armed struggle until the liberation of Palestine and the building of an Islamic state," al-Zawahiri said in the video aired on Saturday.
"Reaching power is not a goal by itself ... and no Palestinian has the right to give away a grain of the soil.
"The seculars in the Palestinian Authority have sold out Palestine for crumbs... Giving them legitimacy is against Islam."
Commenting on Palestine and Iraq, al-Zawahiri said: "We have to be aware of the American game called 'political process.'"
And turning to the cartoons of the Prophet Muhammad that have been printed in a number of European newspapers, al-Zawahiri said: "They did it on purpose and they continue to do it without apologising, even though no one dares to harm Jews or to challenge Jewish claims about the Holocaust nor even to insult homosexuals."
Considered al-Qaida's chief ideologue, al-Zawahiri appeared in the video wearing a black turban and seated in front of a curtained window.
He spoke insistently and waved his right hand to emphasise his words.
"The insults against Prophet Muhammad are not the result of freedom of opinion but because what is sacred has changed in this culture," he said.
"The Prophet Muhammad, prayers be upon him, and Jesus Christ, peace be upon him, are not sacred any more, while Semites and the Holocaust and homosexuality have become sacred."
"The Prophet Muhammad, prayers be upon him, and Jesus Christ, peace be upon him, are not sacred anymore, while Semites and the Holocaust and homosexuality have become sacred"
Al-Qaida deputy leader
An Aljazeera official said someone had given the videotape to the network. He would not elaborate.
Al-Zawahiri, Osama bin Laden's deputy, has issued several video and audiotapes in the past year. His last video came on 31 January in which he threatened a new attack against the United States.
Bin Laden and al-Zawahiri are believed to be in hiding along the Pakistan-Afghan border.
The audio track of the video aired partially by Aljazeera was posted on the internet earlier.