U.S. soldiers patrol Afghan villages asking about Taliban and Haqqani network activity in the area in the Paktika Province, Afghanistan on October 31, 2011. (Joshua Partlow/THE WASHINGTON POST)

One Tuesday evening last month, while patrolling along Afghanistan’s border with Pakistan, American soldiers came under a flurry of gunfire and rocket-propelled grenades from the vicinity of a Pakistani military checkpoint known as Border Post 4.

The soldiers with the 3rd platoon launched a warning flare, called a “red star cluster,” to identify themselves. For a moment, according to a U.S. military summary of the incident, the firing stopped; then it resumed. The U.S. soldiers shot back with their rifles and handheld 60mm mortars — a rare direct-fire engagement with a Pakistani border post.

But as with much concerning Pakistan’s role in the Afghan war, this firefight has left American soldiers at a loss for a clear explanation. It could have been a case of Pakistani soldiers firing on U.S. troops to provide cover for insurgents maneuvering nearby, as some U.S. soldiers initially concluded. Or, insurgents could have been firing from a checkpoint that had already been abandoned by Pakistani troops.

The murky episode is one small illustration of the challenge in defining Pakistan’s involvement with insurgents who are fighting U.S. troops. The longer the Afghan war drags on, the more suspicion mounts that Pakistan’s security services provide a wide range of support for the Taliban and its allies. And with this suspicion, Afghan and American relations with Pakistan continue to deteriorate.

There is no shortage of accusations flying across the border. On the Afghan side, officials regularly accuse Pakistan’s military and intelligence services of using the Taliban to fight a proxy war against the United States, their nominal ally. Afghan leaders say Pakistan’s spies meet with the Taliban leadership, and fund and equip them for the fight in Afghanistan.

With equal conviction, Pakistani officials deny harboring or helping the insurgency in any way and blame U.S. and Afghan officials for allowing insurgent sanctuaries in Afghanistan. Pakistan’s president vowed this month to “eradicate” the Haqqani network, the insurgent group that the U.S. military’s highest-ranking officer this year called a “veritable arm” of Pakistan’s spy agency, the Directorate for Inter-Services Intelligence, or ISI.

On the border, the situation does not become much clearer. U.S. soldiers in Paktika, a province the size of New Jersey that is across from the Pakistani tribal area of North Waziristan, see the role of Pakistan as a somewhat abstract question — they do not let it distract them from the daily requirements of fighting the insurgency.

Several U.S. soldiers here said they believed it was likely that Pakistan’s government was complicit with the Taliban and Haqqani fighters in the province but that they could not prove that connection. Accusing Pakistan of helping to kill U.S. troops — while at the same time receiving billions in American aid — is a politically touchy issue that many U.S. soldiers would rather avoid.

“There’s a lot of smoke. Is there fire?” said one U.S. military officer about possible Pakistani complicity with the insurgents. “It’s a very strong circumstantial argument at this point.”

Inside Forward Operating Base Tillman, in eastern Paktika province, Pakistani soldiers share office space with U.S. troops at a border coordination center that is intended to help bolster efforts against insurgents on both sides of the border. At this base, and others along the border, U.S. troops regularly come under attack from rockets fired from Pakistani territory. About half of all indirect insurgent fire — rockets, mortars or artillery — in the province is launched from within a mile of the border, and 10 to 12 percent of it comes from the Pakistan side, said Maj. Eric Butler, the intelligence officer with the U.S. brigade in Paktika.

American soldiers said the sophisticated and coordinated nature of some rocket-fire suggests extensive training, and perhaps Pakistani military involvement.

Butler said there is “no real, hard evidence that anybody is being complicit.” But he added: “I personally find it very difficult to believe that there’s not some kind of knowledge.”

Lt. Col. Curtis D. Taylor, who commands an American battalion in western Paktika, said there are regular rumors about Pakistan’s involvement with insurgents but that those are unconfirmed.

“If you talk to the people who are connected to the insurgency, they tell you that the insurgent activity . . . the intensity of activity, is modulated by Pakistani ISI,” Taylor said. “That’s consistent across the board. What they tell you is the ISI has control over the intensity of the insurgency.”

The firefight on Oct. 25 remains something of a mystery. After the first few minutes of firing from the Pakistani Frontier Corps checkpoint, U.S. aircraft spotted a group of insurgents about 200 yards to the west firing rocket-propelled grenades at the American soldiers. U.S. military aircraft dropped two 500-pound bombs and killed the insurgents.

When the fighting first broke out, an officer at FOB Tillman asked the Pakistani liaison officer to call his Frontier Corps counterparts, but the Pakistani major was “hemming and hawing,” one U.S. military officer said. When he eventually called, there was no answer.

A report written a day after the fighting suggested that U.S. officers believed Pakistani troops were providing cover for the insurgents by firing at the American soldiers. “It is likely PAKMIL were facilitating [insurgents’] maneuver on [coalition forces] positions,” it read. “It is my assessment that conducting coordinated PAKMIL operations will most likely remain problematic due to perceived support and/or tolerance of [insurgent] forces operating in and around PAKMIL [checkpoints].”

But a few days after the fighting, a group of U.S. Special Operations soldiers went to a hilltop about 400 yards from Border Post 4 and surveyed it with a night-vision scope. It appeared as if it might be abandoned, one U.S. military official said.

The insurgents might have used the checkpoint, if it had been abandoned, for the potential political benefit of ratcheting up tension along the border, the U.S. military official said. Others believe that the checkpoint was occupied and that there had been a Pakistani flag flying from it the day of the attack.

Butler, the brigade intelligence officer, said there is no evidence to prove that Pakistani soldiers were firing that day, but he said it is possible they were.

“I can see how it could have been two different groups of insurgents — one to cover the other — or Pak Mil doing it,” he said. “I have no evidence either way.”