Mr Musharraf, whose support for the US-led war in Afghanistan after the attacks was instrumental in the fall of the Taliban regime, said former deputy secretary of state Richard Armitage made the threat to Pakistan's head of intelligence.
"The intelligence director told me that (Armitage) said, 'Be prepared to be bombed. Be prepared to go back to the Stone Age'," Mr Musharraf said in the interview with the "60 Minutes" investigative news program.
"I think it was a very rude remark," Musharraf says in the interview, due to be broadcast on Sunday. "One has to think and take actions in the interests of the nation, and that's what I did."
White House declines comment
Shortly after the September 11 attacks, Pakistan abandoned its support for the Taliban, which was sheltering Al-Qaeda leaders, and became a front-line ally in the US-led "war on terror."
Pakistan has since arrested several senior Al-Qaeda members including Khalid Sheikh Mohammad, the alleged mastermind of the 2001 attacks.
The South Asian country has also deployed around 80,000 troops on the rugged border with Afghanistan to hunt pro-Taliban and Al-Qaeda linked militants who sneaked into the area after fleeing the US-led invasion of Afghanistan.
The White House declined to comment on Mr Musharraf's comments. A US official said only that Pakistan had made "a strategic choice" to help after the September 11 attacks.
Mr Armitage's alleged threat also demanded that Pakistan turn over border posts and bases for the US military to use in the war in Afghanistan, which ended with the Taliban regime's collapse in late 2001.
Other "ludicrous" demands required Pakistan to suppress domestic expressions of support for militant attacks on US targets, according to the CBS network, which produces "60 Minutes".
"If somebody's expressing views, we cannot curb the expression of views," it quoted Mr Musharraf as saying.
Nuclear embarrassment
In the interview, Mr Musharraf also reveals an embarrassing episode in which former CIA director George Tenet confronted him in 2003 with proof that the father of Pakistan's nuclear program was passing secrets to Libya, Iran and North Korea.
Abdul Qadeer Khan, held as hero in Pakistan for helping to make the country a nuclear power, admitted giving away nuclear secrets in a televised confession in February 2004, exposing a global black market in nuclear technology.
"He (Tenet) took his briefcase out, passed me some papers. It was a centrifuge design with all its numbers and signatures of Pakistan. It was the most embarrassing moment," Mr Musharraf says.
It was only then, he says, that he realised that not only had blueprints been leaked, but that centrifuges themselves -- a crucial element in enriching uranium to weapons grade -- were being passed on, CBS said.
Mr Musharraf denies that anyone in the government or military was aware of the leak.
He pardoned Khan the same month, but the ailing scientist has since lived under virtual house arrest in a leafy diplomatic sector in Islamabad and makes no public appearances.