WASHINGTON — President Bush secretly approved American military raids inside Pakistan against alleged terrorist targets, according to a former intelligence official with recent access to the Bush administration’s debate about how to fight Al Qaeda and the Taliban inside the lawless tribal border area.

The former official spoke today on condition of anonymity to describe the classified order.

A senior American military official last week also 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 American response to rising violence along the Pakistan-Afghanistan border includes discussion of classified intelligence.

The former official told The Associated Press that Bush signed an order over the summer giving new authority to American special operations forces to target suspected terrorists in the dangerous area along the Afghanistan border. 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.

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

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

Mr. Bush’s decision to endorse cross-border attacks from Afghanistan without alerting Islamabad leaves President Asif Ali Zardari of Pakistan 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.

Mr. Zardari and other politicians have called the cross-border attacks unacceptable and a violation of their country’s sovereignty. The powerful but media-shy army leader, General Ashfaq Parvez Kayani, took things a step further yesterday, 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,” General 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 Mr. Bush to commit yesterday 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,” the chairman of the Joint Chiefs of Staff, Admiral Mike Mullen, told the House Armed Services Committee on yesterday. “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 American 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 Qaeda safe haven adjacent to the Afghan border.

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

The Pakistani government is not told about the targets in advance because of concerns that the Pakistani intelligence service and military are infiltrated by Al Qaeda and Taliban supporters who would leak the information, the former official said.

The arrangement is deliberately ambiguous. While the Pakistan government is left in the dark, it also does not want the American government announcing that operations were undertaken without Islamabad’s approval.

“They said, don’t rub our noses in it,” the former official said. “It doesn’t want to look like they are just letting the United States do whatever it wants.”

At the same time, the former official said, the Pakistan government recognizes that its settled areas are increasingly targeted by terrorist and militant attacks emanating from the tribal region and its military is not equipped to counter the threat.