Afghan officials who provided details identified the attacker as police Sgt. Nargas, a mother of four with a clean record. The shooting was outside the police headquarters in a walled compound which houses the governor’s office, courts and a prison in the heart of the capital.

A police official said she was able to enter the compound armed because she was licensed to carry a weapon as a police officer.

The American, whose identity was not released, was a civilian adviser who worked with the NATO command. He was shot as he came out of a small shop, Kabul Governor Abdul Jabar Taqwa told The Associated Press. The woman refused to explain her motive for her attack, he said.

The fact that a woman was behind the assault shocked some Afghans.

“I was very shaken when I heard the news,” said Nasrullah Sadeqizada, an independent member of Parliament. “This is the first female to carry out such an attack. It is very surprising and sad,” he added, calling for more careful screening of all candidates, male and female, for the police force.

According to NATO, some 1,400 women were serving in the Afghan police force mid-year with 350 in the army — still a very small proportion of the 350,000 in both services. Such professions are still generally frowned upon in this conservative society but women have made significant gains in recent years, with most jobs and education opportunities open to them, at least by law if not always in practice.

This is in stark contrast to the repression they suffered under the former Taliban regime, which forced women to be virtual prisoners in their homes, and severely punished them for even small infractions of the draconian codes.

The NATO command said that while the investigation continued, there might be “some temporary, prudent measures put into place to reduce the exposure of our people.” But a NATO spokesman, U.S. Air Force Lt. Col. Lester T. Carroll, said the vital mission of training the Afghan police “remained unchanged.”

There have been more than 60 insider attacks this year against foreign military and civilian personnel. They represent another looming security issue as President Barack Obama and Afghan President Hamid Karzai prepare to meet early next year to discuss the pullout of NATO troops from Afghanistan by 2014 and the size and nature of a residual force the United States will keep in the country.

Insider attacks by Afghan soldiers or police have accelerated this year as NATO forces, due to mostly withdraw from the country by 2014, have speeded up efforts to train and advise Afghan security before the pullout.

The surge in such attacks is throwing doubt on the capability of the Afghan security forces to take over from international troops and has further undermined public support for the war in NATO countries.

It has also stoked suspicion among some NATO units of their Afghan counterparts, although others enjoy close working relations with Afghan military and police.

As such attacks mounted this year, U.S. officials in Kabul and Washington insisted they were “isolated incidents” and withheld details.

An AP investigation earlier this month showed that at least 63 coalition troops — mostly Americans — had been killed and more than 85 wounded in at least 46 insider attacks. That’s an average of nearly one attack a week. In 2011, 21 insider attacks killed 35 coalition troops.

There have also been incidents of Taliban and other militants dressing in Afghan army and police uniforms to infiltrate NATO installations and attack foreigners.

In February, two U.S. soldiers died from an attack by an Afghan policeman at the Interior Ministry in Kabul. The incident forced NATO to temporarily pull out their advisers from a number of ministries and police units and revise procedures in dealing with Afghan counterparts.

More than 50 Afghan members of the government’s security forces also have died this year in attacks by their own colleagues. Taliban militants claim such attacks reflect a growing popular opposition to both foreign military presence and the Kabul government.

In the latest attack, the governor said Nargas, who like many Afghans goes by one name, had asked bystanders where the governor’s office was located before confronting the American.

Interior Ministry spokesman Sediq Sediqi said she fired only one shot that struck the American in the chest. He died either on the way or just upon arrival at a hospital, the spokesman added, describing her act as a “huge crime.” He said the woman attempted to run away, pistol still in hand, after the shooting. But she was subdued by police.

She was taken into Afghan custody and Sediqi said she refused to answer questions after hours of interrogation aimed at determining her motives.

Nargas had worked with a human rights department of the police for two years and had earlier been a refugee in Pakistan and Iran, Kabul Deputy Police Chief Mohammad Daoud Amin said.

She could enter the compound armed because as a police officer, she was licensed to carry a pistol, Amin said. He said he did not know whether the killer and victim were acquainted.

“Her background is very clean. We don’t see that she had any connection with armed insurgent groups,” Sediqi said. He added that she aroused no suspicion because she frequently went back and forth on business between the compound and the Interior Ministry where she worked.

Canadian Brig. Gen. John C. Madower, another NATO command spokesman in Kabul, called the incident “a very sad occasion” and said his “prayers are with the loved ones of the deceased.”

The killing came just hours after an Afghan policeman shot five of his colleagues at a checkpoint in northern Afghanistan late Monday. The attacker then stole his colleague’s weapons and fled to join the Taliban, said deputy provincial governor in Jawzjan province, Faqir Mohammad Jawzjani.

Separately, U.S. military officials were investigating the apparent suicide of a Navy SEAL commander in Afghanistan. A U.S. military official in Washington said Cmdr. Job W. Price, 42, of Pottstown, Pa., died Saturday of a noncombat-related injury in Uruzgan province. The official said the death “appears to be the result of a suicide.”

The official spoke on condition of anonymity because the death is still being investigated.