WASHINGTON — President Bush secretly approved U.S. military raids inside Pakistan against alleged terrorist targets, according to current and former U.S. officials with recent access to the Bush administration’s debate about how to fight al-Qaida and the Taliban inside the lawless tribal border area.

The officials spoke Thursday on condition of anonymity to describe the classified order.

A senior U.S. military official last week confirmed that a special forces attack had taken place about a mile across Pakistan’s border with Afghanistan. That official spoke on condition of anonymity because the internal debate over the U.S. response to rising violence along the Pakistan-Afghanistan border includes discussion of classified intelligence.

The presidential order, first reported by the New York Times, was issued over the summer to give new authority to U.S. special operations forces to target suspected terrorists in the dangerous area along the Afghanistan border, a former intelligence official said. More recently, the administration secretly gave conventional ground troops new authority to pursue militants across the Afghan border into Pakistan, the former official said.

The “rules of engagement” have been loosened, allowing troops to conduct border attacks without being fired on first if they witness attacks coming from the region, the former official said. That would include artillery, rockets and mortar fire from the Pakistan side of the border.

A U.S. official familiar with South Asia said the new rules were adopted in response to increasing frustration with Pakistani counterterrorism cooperation.

This frustration came to head with the discovery of evidence that Pakistan’s intelligence service had been compromised by militants and that some members of the service, known as the ISI, were helping extremists, particularly with the attack on the Indian embassy in Kabul, the official said.

“Up to that point, the idea was to share intelligence with the Pakistanis and then proceed but there was a lot of frustration with delays and problems, including leaks to militants, in sharing the intelligence,” the official said.

“This (the new order) is a reaction to that and it was sped up by the revelations about the penetration of the Pakistani intelligence service,” the official said. “It was decided that we had no choice but to free up the hands of our commanders.”

The new authority allowed last week’s unprecedented U.S.-led ground assault into the volatile region known as the tribal areas. The U.S. forces were apparently seeking specific Taliban or al-Qaida leaders. The senior U.S. military official said the assault targeted “individuals who were clearly associated with attacks on U.S. forces in Afghanistan.”

The Sept. 4 raid left at least 15 people dead, and embarrassed Pakistan’s new civilian-led government. Pakistani officials have also said U.S. forces were involved.

Bush’s decision to endorse cross-border attacks from Afghanistan without alerting Islamabad leaves Pakistani President Asif Ali Zardari with a major foreign policy challenge. He replaced Pervez Musharraf, who had been Washington’s point man in Pakistan but resigned under pressure in August.

Zardari and other politicians have called the cross-border attacks unacceptable and a violation of their country’s sovereignty. Gen. Ashfaq Parvez Kayani, the powerful but media-shy army leader, took things a step further Wednesday, when he said Pakistan’s territorial integrity would be “defended at all cost.’

“Reckless actions” which kill civilians “only help the militants and further fuel the militancy in the area,” Kayani said, reflecting the views of many Pakistanis.

At the crux of the dispute are militant havens that have grown on Pakistan’s side of the border at the same time that a resurgent Taliban has been increasing its attacks inside Afghanistan, leading Bush to commit Wednesday to sending more troops there. Washington wants Pakistan to do more to crack down on its side of the border.

“Until we work more closely with the Pakistani government to eliminate the safe havens from which they operate, the enemy will only keep coming,” Adm. Mike Mullen, chairman of the Joint Chiefs of Staff, told the House Armed Services Committee on Wednesday. “Frankly, we are running out of time.”

Pakistan says it is doing all it can.

Pakistan’s inability or unwillingness to mount a counterinsurgency campaign inside the tribal area was discussed at a National Security Council meeting held this week, according to notes of the meeting provided to The Associated Press. The notes said Pakistan is still focused on fighting India and is “still denying the counterinsurgency problem.”

Top U.S. and Pakistani military officials conducted a secret strategy session in August on an aircraft carrier off Pakistan to discuss the problem.

Senior White House officials this summer were debating whether to adopt a new, more aggressive military stance to attack the maturing al-Qaida safe haven adjacent to the Afghan border.

The old strategy — relying on Pakistan to keep a lid on the tribal areas — was meant to support strong ally Musharraf. The official said Musharraf’s waning fortunes heavily influenced the debate in favor of stronger action.

State Department spokesman Sean McCormack declined to comment on the matter Thursday but said the U.S., Pakistan and the rest of the world share an interest in cracking down on militants along the Pakistani-Afghan border.

“We have clear interests there. The Pakistanis have clear interests, obviously, in combatting the threat of violent extremism in their own country and how that effects others around them and others globally,” he said.