A military investigation has concluded that it took about 45 minutes for a NATO operations officer in Afghanistan to notify a senior allied commander about Pakistan’s calls that its outposts were under attack, one of several breakdowns in communication that contributed to airstrikes that killed 26 Pakistani soldiers last month.

Once alerted, the commander immediately ordered a halt to American attacks on two Pakistani border posts. By then, communications between the two militaries had sorted out a chain of errors and the shooting had stopped. The delay, by at least one officer and possibly a second, raises questions about whether a faster response could have spared the lives of some Pakistani soldiers.

Officials “did not respond correctly, quickly enough or with the sense of urgency or initiative required given the gravity of the situation and the well known sensitivity surrounding the Afghan-Pakistan border region,” the report found.

An unclassified version of the report, released Monday by the military’s Central Command, also revealed for the first time that an American AC-130 gunship flew two miles into Pakistan’s airspace to return fire on Pakistani troops who had attacked a joint American-Afghan ground patrol just across the border in Afghanistan.

The 30-page report, which expanded upon a briefing last week by the chief investigator, Brig. Gen. Stephen A. Clark of the Air Force, also found that competing NATO and American rules of engagement related to operations along the border “lacked clarity and precision, and were not followed.”

The full report alters and expands upon the impression of the inquiry’s findings created by General Clark’s briefing, which had emphasized how checks on both sides failed. Among the reason the checks failed, he said, were because American officials did not trust Pakistan enough to give it detailed information about American troop locations in Afghanistan, and Pakistan had not informed NATO of the locations of its new border posts.

The details released Monday add to those failures unexplained delays and a lack of urgency by NATO officers in notifying their superiors of the unfolding late-night debacle that has plunged relations between the two countries to new lows.

In a statement on Monday, Gen. James N. Mattis, who leads the Central Command, directed the top allied officer in Afghanistan, Gen. John R. Allen, to carry out most of the recommendations “as soon as operationally possible.”

The episode, the worst in nearly a decade of fatal cross-border mistakes, exposed the flaws in a system devised to avoid such mistakes. The report criticized an allied practice, in place since at least August, of not divulging to Pakistan the precise location of allied ground troops in Afghanistan for fear Pakistan might jeopardize their operations.

In his briefing last week, General Clark outlined a series of miscommunications on both sides that he said contributed to the accident. But the report offered new details.

At 12:35 a.m. on Nov. 26, about halfway through the episode, a NATO liaison officer in Pakistan notified the night director in an allied operations center in Afghanistan that Pakistan said its troops were under attack, presumably from NATO aircraft. The liaison officer did not alert a top general in Afghanistan, Maj. Gen. James Laster, until 1:20 a.m., after the firefight had ended.

Before the mission began, General Laster had ordered two precautions to reduce the risk of accidental contact. He moved the ground patrol’s helicopter landing zone farther away from the Pakistani border, and he requested the location of any nearby Pakistani outposts. The list he received was outdated.

Pakistan has insisted that its forces did nothing wrong, and that they did not fire the first shots. Senior Pakistani military and civilian officials have accused the United States of intentionally striking the border posts, even after Pakistani officers called their counterparts to complain that they were under allied attack.

General Clark’s report acknowledged that a pivotal allied mistake was not informing Pakistan about the patrol. Without that warning, the Pakistani soldiers would not have known to expect allied forces nearby. NATO and Pakistani forces are supposed to inform each other about operations on the border to avoid this kind of mistake.