The BBC's Paul Adams in Washington says despite the fears generated by the Christmas Day attempted bombing, the US administration is at pains to play down any suggestion al-Qaeda is a growing threat.
The voice recording - which said it was from "Osama to Obama" - claimed al-Qaeda was behind the plot, and warned of further attacks.
Broadcast on al-Jazeera TV on Sunday, it said a Nigerian man, Umar Farouk Abdulmutallab, who is charged with attempting to blow up the airliner, was a "hero".
But in the interview which aired on ABC on Tuesday, Mr Obama said: "Al-Qaeda itself is greatly weakened from where it was back in 2000.
The authenticity of the audio tape has not been verified. Courtesy al-Jazeera
"Bin Laden sending out a tape trying to take credit for a Nigerian student who engaged in a failed bombing attempt is an indication of how weakened he is, because this is not something necessarily directed by him."
On Monday, the US state department's co-ordinator for counter-terrorism said the "Bin Laden" audio tape was an attempt to bask in "reflected glory" of the plot.
The Yemen-based regional wing of al-Qaeda has said it was behind the attempted attack.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.