3 added 72 characters in body
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Although he initially denied involvement he later claimed responsibility, according to the New York Times reporting on a video released by Bin Laden in 2004:

[Bin Laden] accused Mr. Bush of "misleading" the American people three years after the Sept. 11 attacks, the Al Jazeera Web site said, and added that "we decided to destroy towers in America" because "we want to regain the freedom of our nation."

The Associated Press said Mr. bin Laden also went on to say in the videotape: "God knows that it had not occurred to our mind to attack the towers, but after our patience ran out and we saw the injustice and inflexibility of the American-Israeli alliance toward our people in Palestine and Lebanon, this came to my mind."

Bin Laden Takes Responsibility for 9/11 Attacks in New Tape

So one way orUPDATE: This answer was posted in response to the other, heoriginal question which asked whether Bin Laden was not consistentboth immediate and consistent in denying involvement. 

Although he initially denied involvement he later claimed responsibility, according to the New York Times reporting on a video released by Bin Laden in 2004:

[Bin Laden] accused Mr. Bush of "misleading" the American people three years after the Sept. 11 attacks, the Al Jazeera Web site said, and added that "we decided to destroy towers in America" because "we want to regain the freedom of our nation."

The Associated Press said Mr. bin Laden also went on to say in the videotape: "God knows that it had not occurred to our mind to attack the towers, but after our patience ran out and we saw the injustice and inflexibility of the American-Israeli alliance toward our people in Palestine and Lebanon, this came to my mind."

Bin Laden Takes Responsibility for 9/11 Attacks in New Tape

So one way or the other, he was not consistent.

Although he initially denied involvement he later claimed responsibility, according to the New York Times reporting on a video released by Bin Laden in 2004:

[Bin Laden] accused Mr. Bush of "misleading" the American people three years after the Sept. 11 attacks, the Al Jazeera Web site said, and added that "we decided to destroy towers in America" because "we want to regain the freedom of our nation."

The Associated Press said Mr. bin Laden also went on to say in the videotape: "God knows that it had not occurred to our mind to attack the towers, but after our patience ran out and we saw the injustice and inflexibility of the American-Israeli alliance toward our people in Palestine and Lebanon, this came to my mind."

Bin Laden Takes Responsibility for 9/11 Attacks in New Tape

UPDATE: This answer was posted in response to the original question which asked whether Bin Laden was both immediate and consistent in denying involvement. 

2 added 72 characters in body
source | link

YesAlthough he initially denied involvement he later claimed responsibility, according to the New York Times, reporting on a video released by Bin Laden in 2004:

[Bin Laden] accused Mr. Bush of "misleading" the American people three years after the Sept. 11 attacks, the Al Jazeera Web site said, and added that "we decided to destroy towers in America" because "we want to regain the freedom of our nation."

The Associated Press said Mr. bin Laden also went on to say in the videotape: "God knows that it had not occurred to our mind to attack the towers, but after our patience ran out and we saw the injustice and inflexibility of the American-Israeli alliance toward our people in Palestine and Lebanon, this came to my mind."

Bin Laden Takes Responsibility for 9/11 Attacks in New Tape

So one way or the other, he was not consistent.

Yes, according to the New York Times, reporting on a video released by Bin Laden in 2004:

[Bin Laden] accused Mr. Bush of "misleading" the American people three years after the Sept. 11 attacks, the Al Jazeera Web site said, and added that "we decided to destroy towers in America" because "we want to regain the freedom of our nation."

The Associated Press said Mr. bin Laden also went on to say in the videotape: "God knows that it had not occurred to our mind to attack the towers, but after our patience ran out and we saw the injustice and inflexibility of the American-Israeli alliance toward our people in Palestine and Lebanon, this came to my mind."

Bin Laden Takes Responsibility for 9/11 Attacks in New Tape

Although he initially denied involvement he later claimed responsibility, according to the New York Times reporting on a video released by Bin Laden in 2004:

[Bin Laden] accused Mr. Bush of "misleading" the American people three years after the Sept. 11 attacks, the Al Jazeera Web site said, and added that "we decided to destroy towers in America" because "we want to regain the freedom of our nation."

The Associated Press said Mr. bin Laden also went on to say in the videotape: "God knows that it had not occurred to our mind to attack the towers, but after our patience ran out and we saw the injustice and inflexibility of the American-Israeli alliance toward our people in Palestine and Lebanon, this came to my mind."

Bin Laden Takes Responsibility for 9/11 Attacks in New Tape

So one way or the other, he was not consistent.

1
source | link

Yes, according to the New York Times, reporting on a video released by Bin Laden in 2004:

[Bin Laden] accused Mr. Bush of "misleading" the American people three years after the Sept. 11 attacks, the Al Jazeera Web site said, and added that "we decided to destroy towers in America" because "we want to regain the freedom of our nation."

The Associated Press said Mr. bin Laden also went on to say in the videotape: "God knows that it had not occurred to our mind to attack the towers, but after our patience ran out and we saw the injustice and inflexibility of the American-Israeli alliance toward our people in Palestine and Lebanon, this came to my mind."

Bin Laden Takes Responsibility for 9/11 Attacks in New Tape