It was not clear when the videos were filmed, but Ayman al-Zawahri, bin Laden's deputy in Al-Qa'ida was shown claiming the 11 September attacks as a "great victory."
Al-Jazeera editor-in-chief Ibrahim Hilal said the excerpts were from an hour-long video, complete with narration and graphics, delivered by hand to the station's Qatar offices a week ago.
"I can't tell you about when the material was made exactly but it seems very recent," Mr Hilal said, noting the narrator at one point refers to the 27-28 March Arab League summit as coming up shortly.
Al-Jazeera showed only brief clips and said it would air the complete tape on Thursday.
Mr Hilal would not elaborate on how the channel got the tape, which Al-Jazeera said came with the title: "The wills of the New York and Washington Battle Martyrs." The title shot included pictures of the 19 hijacking suspects. he said the tape Al-Jazeera had showed only one of the 19 speaking.
"We got it from our sources, it got to us. We are expecting other tapes from the same source, so it is not good to" reveal the source, he said, adding that the tape might be from inside Afghanistan.
In one of the excerpts, bin Laden and al-Zawahri kneel side-by-side before a lush background that appeared to be a photograph. Only al-Zawahri was shown speaking.
"Those 19 brothers who went out and worked and sacrificed their lives for God, God granted this conquest that we enjoy today," he said. "The great victory that was achieved was because of God's help and not because of our efficiency or power."
The other excerpt showed the man identified as one of the 11 Septemberr hijackers speaking to the camera in a style similar to that in videotapes made by Palestinian suicide bombers before attacks.
Al-Jazeera said in a press release that the tape indicated the attacker's statement was recorded in Kandahar, Afghanistan, six months earlier "and is considered to be the first evidence linking bin Laden and Al-Qa'ida network to the attacks."
An Al-Jazeera subtitle identified the man only as Alghamdi. Mr Hilal said that referred to the tribe of a hijacker the FBI has identified as Ahmed Ibrahim A. Al Haznawi. Al Jazeera said it identified Al Haznawi from photographs of the hijackers on the FBI website.
US officials say Al Haznawi was one of four attackers on United Airlines Flight 93, which crashed in rural Pennsylvania.
In the video, the man identified as the suicide hijacker said: "It's time to kill Americans in their heartland."
He wore military fatigues over a black shirt and a black-and-white checked scarf wrapped around his head. He sat before what appeared to be a photo montage showing the World Trade Center in flames. Al-Jazeera said that recording was made months before the attack, but did not explain how it reached that conclusion.
Also from the Asia China section. 140 die in Korean plane crash