The aircraft, with 290 people on board, was flying from Amsterdam, Netherlands.
Abdulmutatallab allegedly had explosives stitched into his underwear, which failed to detonate aboard the Northwest Airlines flight.
Passengers prevented the attack, tackling and restraining Abdulmutallab before he was escorted off the plane.
The footage appears to show Abdulmutallab, dressed in a white linen shirt and white skullcap as he speaks to the camera, saying "your brotherhood of Muslims in the Arabian peninsula has the right to wage jihad because the enemy is in your lands with their armies, the Jews and the Christians and their agents".
"He reads several passages from the Koran and adds, 'God said those who punish you must be punished,'" ABC reported.
The videos appear to support Abdulmutallab's statements to the FBI after his arrest that "others like me" in Yemen were training to carry out attacks against Western targets.
Earlier this month, Miriam Siefer, the state-appointed lawyer for Abdulmutallab, declined to comment on reporters' questions about a potential plea deal or the extent to which Abdulmutallab is co-operating with government officials.
Abdulmutallab pleaded not guilty in January to six terrorism-related charges, including attempted murder of the passengers and trying to use a weapon of mass destruction.
He faces a maximum penalty of life imprisonment if convicted.
The foiled bombing has triggered global alarm, leading the US to adopt stringent new screening and security measures at airports around the world.
Officials say US intelligence suggests Abdulmutallab was an extremist and that al-Qaeda in the Arabian Peninsula was plotting an attack, but no action was taken.
Against this backdrop, Janet Napolitano, the US homeland security secretary, has told domestic and international aviation leaders that her department will bolster global aviation security.
"We are committed to working closely with our partners around the world to deploy intelligence-based targeting, state-of-the art technologies and proactive screening measures to deter and disrupt terrorism and other threats to the global aviation system," she said.