In the clip shown on Britain's Channel 4 television, Khan urged British Muslims to take part in jihad, "holy war" or "spiritual struggle", and accused "so-called community leaders" of being "content with their Toyotas and their semi-detached houses."
Khan, widely regarded as the ring-leader of the group that killed 52 commuters and injured about 700, has previously been seen on video blaming the British public for the July 7 attacks on the capital's transport network.
In the latest extract, followed by a message from Al-Qaeda's deputy leader, Ayman Al-Zawahiri, Khan said: "Jihad is an obligation on every single one of us, men and women, and by staying at home you are turning your backs on jihad, which is a major sin."
He added: "Our so-called scholars today are content with their Toyotas and their semi-detached houses.
"They tell us ludicrous things like 'you must obey the law of the land.' How on earth did we conquer lands in the past if we were to obey by this law? By Allah, these scholars will be brought to account.
"If they fear the British Government more than they fear Allah, then they must desist in giving talks, lectures and passing fatwas and they need to stay at home, they're useless, and leave the job to the real men, the true inheritors of the prophet (Mohammed)."
Al-Zawahiri is then heard to say: "These are the scholars of beggary, working to beg the pleasure of (Queen) Elizabeth, head of the Church of England."
The Al-Qaeda number two also branded the British queen one of Islam's "severest enemies."
Nazir Ahmed, a member of Britain's upper chamber of parliament, the House of Lords, rejected Khan's comments, telling the programme: "The jihad that you must do is become a good citizen and good member of the community. These people misinterpret the Koran and take it out of context."
Khan, 30, died with six other people when the explosives he was carrying exploded on an underground train carriage at Edgware Road station.