The classified orders reflect concern about safe havens for Al-Qaeda and the Taliban inside Pakistan, as well as an American view that Pakistan lacks the will and ability to combat militants, the newspaper said in a dispatch from Washington.
"The situation in the tribal areas is not tolerable," said a senior US official who spoke to the Times on condition of anonymity. "We have to be more assertive. Orders have been issued."
The newspaper said the orders also illustrated lingering distrust of the Pakistani military and intelligence agencies and a belief some US operations had been compromised once Pakistanis were advised of the details.
US officials told the Times they would notify Pakistan when they conduct limited ground attacks like the special operations raid last week in a Pakistani village near the Afghanistan border, but they would not ask for its permission.
The story about Bush's new orders appeared a day after the Pakistan Army Chief, Gen Ashfaq Parvez Kayani, said that his forces would not tolerate American incursions like the one that took place last week and that the army would defend the country's sovereignty "at all costs."
"The sovereignty and territorial integrity of the country will be defended at all cost and no external force is allowed to conduct operations ... inside Pakistan," a military statement quoted Kayani as saying.
The Times wrote, "It was unclear precisely what legal authorities the United States has invoked to conduct even limited ground raids in a friendly country."
A senior US official told the Times the Pakistani government had assented privately to the general concept of limited ground assaults by US forces against significant militant targets, but that it did not approve each mission.
"Any new ground operations in Pakistan raise the prospect of American forces being killed or captured in the restive tribal areas - and a propaganda coup for Al-Qaeda," the Times said. "Last week's raid also presents a major test for Pakistan's new president, Asif Ali Zardari, who supports more aggressive action by his army against the militants ... "
The top US military officer told Congress on Wednesday the military was not winning the fight against the insurgency in Afghanistan and said it would revise its strategy to combat militants safe havens in Pakistan.
"I'm not convinced we are winning it in Afghanistan. I am convinced we can," Adm Mike Mullen, chairman of the Joint Chiefs of Staff, told a congressional committee nearly seven years after US-led forces toppled the Taliban.
Mullen said he was "looking at a new, more comprehensive strategy for the region" that would cover both sides of the border, including Pakistan's tribal areas.
Violence in Afghanistan has soared over the past two years as al-Qaeda and Taliban fighters have regrouped in the remote region between Afghanistan and Pakistan.
The United States has stepped up attacks against militant targets inside Pakistan this year with a series of missile strikes from unmanned drones and a raid by helicopter-borne US commandos in recent days. The attacks have been widely denounced by Pakistani leaders.