"I am not only grieved, the whole nation is grieved," he said. The hunt for those responsible has made "considerable progress," Malik added, although he gave few details of the investigation.
Authorities have forensic evidence, Malik said.
Police Chief Gul Afzal Afridi of the Swat District said that 60 suspects are being detained, interrogated or investigated.
"We have sufficient evidence to find the culprits," the chief said. "Soon we will catch them."
Politicians and commentators in Pakistan have slammed the attack. But the condemnation of the Taliban has not been as universal.
"Everybody was angry that it happened, but not everybody was angry with the Taliban," said Tazeen Javed, an Islamabad-based communications consultant who writes for The Express Tribune newspaper.
The cricket star-turned-politician Imran Khan, who visited Malala in a hospital in Peshawar last week, has drawn criticism for not condemning the Taliban outright for the attack.
Khan "showed a lot of concern but couldn't resist bringing in the issue of the drone strikes as a cause for this attack, which was a bit of a deflection," said Rumi, referring to the drone attacks carried out by the United States in northwestern Pakistan that have generated resentment in the country.
Certain commentators have also begun to question the official version of events, suggesting that the attack on Malala may be used as a pretext by the government for military action against the Taliban in the restive tribal region of North Waziristan.
"The Malala incident is the CIA's latest attempt to divide public opinion and incite conflict in Pakistani society," Haider Mehdi, a contributor to the Pakistani daily The Nation, wrote in a column Tuesday.
As the controversy about the attack rages in Pakistan, the doctors treating Malala thousands of miles away said they are "very pleased" with her progress and optimistic that she will make a good recovery.
However, she faces reconstructive surgery and there is "still a long way to go," said Rosser, of the Queen Elizabeth Hospital in Birmingham.
Her family is not yet in England to be by her bedside, but the Pakistani high commissioner is making arrangements on that front, he said.
In the meantime, the 14-year-old appears to be "every bit as strong as we had been led to believe," Rosser said, adding that the consultant leading her care "is impressed by her resilience and her strength."