A profound lack of trust between the United States and Pakistan was a key factor leading to U.S. airstrikes last month that killed 24 Pakistani soldiers, according to the results of a Pentagon investigation of the incident.

That mutual mistrust produced what a Pentagon spokesman Thursday called “tragic results.” American forces did not tell their Pakistani counterparts that they planned a ground raid on an Afghan border village because U.S. officials suspect Pakistan uses such information to warn insurgents. Alarmed at activity near their border post, Pakistani soldiers began firing into the darkness. In response, the Americans launched an air attack.

When the Pakistanis called U.S. commanders to implore them to stop, the Americans refused to reveal the exact coordinates of the airstrikes because of the “overarching lack of trust,” according to Air Force Brig. Gen. Stephen A. Clark, who conducted the investigation. Instead, U.S. forces transmitted a “general location,” which Clark said turned out to be wrong.

Despite the acknowledged mistakes, the investigation found that “U.S. forces, given what information they had available to them at the time, acted in self-defense and with appropriate force after being fired upon,” Pentagon spokesman George Little said.

Little said there was no “intentional effort” to target the Pakistani military or to “deliberately provide inaccurate location information.” But he expressed “our deepest regret” for the deaths.

“We cannot operate effectively on the border — or in other parts of our relationship — without addressing the fundamental trust still lacking between us,” the White House said in a statement. “The lesson going forward is that we need to broaden cooperation and increase understanding between our two countries.”

Neither the investigation nor the expression of regret is likely to satisfy Pakistan, which has called for a U.S. apology and said the attack — three airstrikes, over 90 minutes, by an AC-130 gunship and Apache attack helicopters — was deliberate.

In a brief text message, the Pakistani military said it “does not agree with the findings of the US/NATO inquiry as being reported in the media. The inquiry report is short on facts. Detailed response will be given as and when the formal report is received.”

In response to the air attack, Pakistan shut one of the vital border crossings NATO uses to ship supplies into Afghanistan and recalled some of the military liaison officers who work alongside NATO officials in Afghanistan.

The decision to ascribe fault to both sides and express only regret exacerbated tensions between the Pentagon and the State Department. Diplomats had appealed to the White House to issue a presidential apology and had pushed for more conciliatory language in summing up the findings.

Little said the United States would provide Pakistan with the report, which was described by Clark in a Pentagon news conference but not publicly released. Defense officials said payments would be offered to the families of the 24 deceased Pakistani soldiers.

Asked whether he had recommended any punishments for the incident, Clark said that was not his job and added that any subsequent action would be “handled within the chain of command.”

Pakistan’s refusal to participate in the investigation meant that “a significant element is missing,” Clark said. “There are always two sides to an event,” and the inquiry “would have been facilitated greatly had Pakistan decided to participate.”

Pakistan has issued repeated public denials that its forces fired first at the Americans. But senior Pakistani defense officials acknowledged to The Washington Post after the incident that soldiers at the border post, located atop a ridgeline looking down at Afghanistan, initiated fire at what they thought were infiltrating militants.

Although the United States has long accused Pakistan of allowing insurgents to cross the border into Afghanistan, Pakistan has said that Afghanistan-based militants move in the other direction. Without being informed of U.S. operations in the area that night, Pakistani officials said, they had no way of knowing who was walking stealthily in the hills near their post.

According to a timeline provided by Clark, a team of about 120 U.S. and Afghan personnel had planned to raid a village close to the Pakistani border on the night of Nov. 25.

U.S. and Afghan forces were taken by helicopter to a landing zone less than two miles from the border, arriving at 9:40 p.m. local time, Clark said. They then walked the rest of the way along what he called the equivalent of “goat trails” through “steep and rugged terrain,” eventually splitting into two groups.

“At 11:09 p.m., they received the first fire” from “heavy machine guns” on a ridgeline to the east, Clark said.

The ground commander “calls back to headquarters for confirmation that there is no Pakistani military in the area” and directs a “show of force” from aircraft already hovering above. The aircraft fires flares, but this “does not cause the machine guns to cease firing,” and the air attack begins. Clark said the flares and a flyover by an F-15 should have signaled the presence of U.S. forces.

“This is the first point where we found a series of miscommunications,” Clark said. The response to the request for information about Pakistani forces, he said, was that “we are checking. . . . That was heard as ‘no Pakistani military in the area’ ” by the operational commander, he said.

Had that communication been correctly received, Clark said, it “may have stopped” the air attack. Pakistan and the United States dispute whether the border post appeared on maps available to both sides.

The first air attack, he said, continued for about six minutes. “Later, they were still receiving some fire” from the Pakistani positions at 11:44 p.m., “and a second engagement occurs,” lasting until about midnight.

“In the background, there are a series of telephone calls from [Afghanistan-based Pakistani liaison officers] to say that their forces are under fire. Confusion was caused by this because of a lack of precision” from the Pakistani side as to the exact location where the soldiers were taking fire. The Pakistani answer, he said, was: “Well, you know where it is, because you are shooting at them.”

“People are trying to do the right thing and nail down specifics so that they can take action,” Clark said. U.S. forces declined to supply the Pakistanis with the exact coordinates, instead giving them a general location and asking whether that was where their forces were located. But the U.S. technician had applied the coordinates to the wrong map — the location he described was about 8.5 miles off — and Pakistan said no.

A third engagement occurred from midnight until just before 1 a.m., Clark said, when a heavy machine gun was located on the Pakistani side “a little further north” of the site from where the Pakistanis first fired. Clark did not make clear whether the machine gun was actually firing at the time.

Systems set up after earlier incidents to prevent or quickly “deconflict” such clashes failed, Clark said, “because of an evolving lack of trust” and a “perception from ISAF [the NATO force in Afghanistan] that the Pakistanis are reticent to give full disclosure on all their border locations for one thing, and, two, that [ISAF is] under the impression that when they have shared information, specific operations have been compromised.”

Londoño reported from Kabul. Staff writer Greg Jaffe in Washington and special correspondent Shaiq Hussain in Islamabad, Pakistan, contributed to this report.