DERA ISMAIL KHAN, Pakistan — Pakistani troops and a NATO helicopter that crossed into Pakistani territory exchanged fire on Tuesday, wounding two soldiers, local officials said, and Pakistan protested, further straining relations with the West following the U.S. raid that killed Osama bin Laden.

Also Tuesday, the army said a “senior al-Qaida operative” had been arrested in the port city of Karachi. In a brief statement, it said Yemeni national Muhammad Ali Qasim Yaqub, alias Abu Sohaib Al Makki, had been working directly under al Qaida leaders along the border between Pakistan and Afghanistan. It did not say when he was arrested.

It was not immediately possible to locate any independent information about Al Makki.

Pakistan’s army and intelligence agencies have faced intense international suspicions since bin Laden was killed on May 2 in an American raid on a large house in the army town of Abbottabad not far from the capital. Many American lawmakers have said bin Laden’s location was a strong sign that Pakistan was playing a “double game” — that is accepting U.S. aid but also protecting terrorists. Pakistan denies that.

The NATO firing incident took place in the Datta Khel area of the North Waziristan tribal region, a known sanctuary for Taliban and al-Qaida militants that launch attacks inside Afghanistan as well as Pakistan. It has been targeted repeatedly by covert U.S. drone strikes.

A Western military official in Afghanistan and a NATO spokesman said there was firing at the border, but they did not confirm that Pakistani border troops were the target or had been hit.

The Pakistani army, facing internal criticism for failing to detect or stop the unilateral American raid that killed bin Laden, said it lodged a strong protest and demanded a meeting with NATO officials to discuss the incident. NATO said it would investigate.

A similar event last year in which two Pakistani soldiers were killed prompted the army to immediately close a key border crossing to NATO supplies heading from Pakistan into landlocked Afghanistan, dramatically exposing the vulnerability of the war effort.

The Western military official said a NATO base in Afghanistan took intermittent direct and indirect fire from the Pakistani side of the border. Two helicopters flew into the area, and one fired across the border after twice taking fire from the Pakistani side, said the official, speaking on condition of anonymity because of the sensitivity of the issue.

NATO declined to say which coalition country was involved, but most of the helicopters that fly in that part of Afghanistan are American.

Relations between the United States and Pakistan have been tense since the Navy SEALs raid on May 2.

The Pakistani government is outraged that the U.S. carried out the operation without telling Pakistan first, and many U.S. officials have expressed disbelief that bin Laden could have lived in Abbottabad for at least five years without the authorities’ knowledge.

NATO said it was still trying to determine whether the helicopter crossed in to Pakistani airspace.

“We’re investigating the incident to determine a flight path by examining GPS waypoints in the helicopter computer, to construct a sequence of events and ultimately determine what led to the exchange of fire,” said Dorrian, the NATO spokesman.

Dorrian said NATO will work with the Pakistani government to determine what happened, saying they expect it will reflect the same good cooperation seen in recent military operations along the border. In recent weeks, NATO and Pakistan have launched coordinated offensives against militants on their respective sides of the border.

“This is going to be transparently looked into,” Dorrian said.

The Pakistani army said in a statement that its troops fired on the helicopter after it entered Pakistani airspace in the early hours of the morning. Two of its troops were injured when the helicopter returned fire, it said.

The helicopter attack came a day after U.S. Sen. John Kerry wrapped up a 24-hour visit to Islamabad in which he worked to salvage the relationship with Pakistan, but also warned the government that “actions, not words” were needed to get ties back on track. Kerry was the most high-profile American to visit Pakistan since the raid on bin Laden.

Kerry said Pakistan had agreed to immediately take several “specific steps” to improve ties, but did not say what they were. The only tangible signs of progress were a remark by Kerry that Pakistan had agreed to give America the tail of a classified stealth helicopter destroyed by U.S. commandos when it malfunctioned during the raid and an announcement that Secretary of State Hillary Rodham Clinton would soon announce a trip to the country.

But there have also been signs of Pakistan’s anger.

The Pakistani government sent the United States a written request following the bin Laden raid, asking Washington to reduce the number of American military personnel in the country, said a U.S. military official Tuesday, speaking on condition of anonymity because of the sensitivity of the issue.

There are currently more than 200 U.S. military personnel in Pakistan, some of whom are tasked with training Pakistani troops, said the official. Pakistan has asked the U.S. to reduce the number of trainers in the country, but the official would not specify the numbers involved.

Also Tuesday, Pakistani security forces shot and killed four would-be suicide bombers, including three women, when they tried to attack an army checkpoint in the southwestern city of Quetta, said Daood Junejo, the city police chief. A fifth suicide bomber detonated his explosives but did not injure anyone, the police chief said.

Security forces stopped the five as they approached the checkpoint in a car, said Junejo. One of the men got out of the car and blew himself up. The other four, who were also wearing suicide vests, were shot when they tried to lob grenades, he said.

However, local TV footage showed what appeared to be security forces shooting at two of the women as they were laying on the ground, one of them with her hand raised over her head.