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ISLAMABAD, Pakistan (CBS News) ― The assassination of his chief political rival was her own fault, Pakistani President Pervez Musharraf tells Lara Logan in his first one-on-one interview since the death of Benazir Bhutto.

The exclusive interview will be broadcast on 60 Minutes on Sunday evening, Jan. 6.

In the interview that took place in Pakistan Saturday morning, Musharraf tells Logan, "For standing up outside the car, I think it was she to blame alone. Nobody else. Responsibility is hers." Bhutto was killed in the Pakistani city of Rawalpindi last week while standing up in a moving car with her head through the roof hatch.

A suicide bomber blew himself up near her car at the time of her death and the government of Pakistan initially said the concussion of the blast caused her to hit her head on the roof hatch. There was also a gunman present, but it's not known whether his shots hit Bhutto.

Asked by Logan if he believes a gunshot could be the cause of Bhutto's head injury, he replies, "Yes, yes."

"So she may have been shot?" asks Logan.

"Yes, absolutely, yes. Possibility," says Musharraf.

Some also speculate that Bhutto, who was campaigning for prime minister in Musharraf's government, had inadequate security.

"Even with the benefit of hindsight, you feel that you and your government did everything possible to give Benazir Bhutto the security she needed?" asks Logan.

Musharraf insists he did. "Yes, yes absolutely. And you have to remember she had the threat. So she was given more security than any other person."

On Saturday, Benazir Bhutto's widowed husband accused members of Pakistan's ruling regime of involvement in his wife's killing and called for a U.N. investigation, as British officers aiding Pakistan's own probe pored over the crime scene.

"An investigation conducted by the government of Pakistan will have no credibility, in my country or anywhere else," Asif Ali Zardari, the effective leader of Bhutto's opposition party, said in a commentary published in The Washington Post. "One does not put the fox in charge of the hen house."

Calls for an independent, international investigation have intensified since the former prime minister was killed Dec. 27 in a shooting and bombing attack after a campaign rally. Opposition activists denounced the government's initial assessment that an Islamic militant was behind the attack and that Bhutto died, not from gunshot wounds, but from the force of the blast.

Musharraf acknowledged that investigators may have drawn conclusions too quickly and mishandled evidence, including hosing down the site hours after the attack. But he insisted the government was competent to run the investigation with the help of forensic experts from Britain's Scotland Yard. The United States said it did not believe a U.N. investigation was needed.

The British investigators arrived at the site of the attack in the city of Rawalpindi under heavy police guard in a convoy of sports utility vehicles. They spoke to local security officials and repeatedly walked from the park where Bhutto held her final campaign rally to the spot outside where her departing vehicle was attacked.

Local police parked a truck where Bhutto's had been, and the British investigators took photographs of it and filmed it from different angles, including from a nearby rooftop.

Zardari said no government investigation would satisfy him. He reiterated his demand for a U.N. probe modeled on the investigation into the death of former Lebanese Prime Minister Rafik Hariri and urged "friends of democracy in the West, in particular the United States and Britain, to endorse the call for such and independent investigation."

"Those responsible - within and outside of government - must be held accountable," he wrote.

Also Saturday, the government accused a leading international think tank of "promoting sedition" for urging Musharraf, a key U.S. ally in the war on terror, to resign.

The report by the Brussels-based International Crisis Group called Musharraf "a serious liability, seen as complicit" in Bhutto's death.

In a statement, the government said the report "amounts to promoting sedition" and the group "neither has the credentials, nor the credibility and lacks representational standing specially on Pakistan's national affairs" to comment on Pakistan.

Also Saturday, gunmen shot and killed one paramilitary soldier and wounded two others in the southwestern city of Quetta, said Rahmatullah Niazi, a senior police official. The motive behind the attack was not known, he said.

(© 2010 CBS Broadcasting Inc. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. The Associated Press contributed to this report.)