But there was no mention of the International Humanitarian Fact-Finding Commission.

"President Obama expressed regret over the tragic incident and offered his thoughts and prayers on behalf of the American people to the victims, their families, and loved ones," the White House statement said.

"Acknowledging the great respect he has for the important and lifesaving work that MSF does for vulnerable communities in Afghanistan and around the world, the President assured Liu of his expectation that the Department of Defense investigation currently underway would provide a transparent, thorough and objective accounting of the facts and circumstances of the incident."

The Doctors Without Borders chief acknowledged Obama's apology, but doesn't want him to stop there. She pushed for the United States to allow an international investigation.

"We reiterate our (request) that the U.S. government consent to an independent investigation led by the International Humanitarian Fact-Finding Commission to establish what happened in Kunduz, how it happened, and why it happened," Liu said.

For charity, 'the biggest loss of life ... in an airstrike'

The attack in the embattled city Saturday killed 12 medical staff members and at least 10 patients, three of them children. It was "the biggest loss of life for our organization in an airstrike," Liu said.

Another 37 people were wounded, according to the global charity group, which works in conflict zones to help victims of war and other tragedies.

Gen. John Campbell, commander of U.S. forces in Afghanistan, has said the hospital was hit accidentally during an American airstrike. The Pentagon is carrying out an investigation, as are NATO and Afghanistan.

"If errors were committed, we will acknowledge them," Campbell said. "We will hold those responsible accountable, and we will take steps to ensure mistakes are not repeated."

Doctors Without Borders said it wants a full and transparent investigation by an independent agency.

"Their description of the attack keeps changing -- from collateral damage, to a tragic incident, to now attempting to pass responsibility to the Afghanistan government," the group said.

U.S. general.: We need new Afghanistan plan

'Today, we say, 'Enough''

The United States has changed its account of what brought on the airstrike.

First, U.S. officials said that initial reports indicated the airstrike was called to protect U.S. forces. Then it said Afghan forces called for the air support because the Afghans were taking fire.

"Today, we say, 'Enough,' " Liu said.

"Today we are fighting back for the respect of the Geneva Conventions. As doctors, we are fighting back for the sake of our patients."

It's an open question as to whether the International Humanitarian Fact-Finding Commission could initiate an inquiry. The panel's website says it requires the consent of the parties involved, and neither the United States nor Afghanistan recognizes the commission.

Jason Cone, the U.S. executive director for Doctors Without Borders, called on one of the 76 nations that recognize the panel to press the issue on the charity's behalf, though none of the 76 had stepped forward as of midday Wednesday. He said the changing U.S. accounts of the strikes underscore the need for an independent inquiry.

Cone paid tribute to the doctors who he said carried on treating the wounded while watching their colleagues die and while the hospital burned.

"In Kunduz, our patients burned in their beds, our doctors' nurses and other staff were killed as they worked, our colleagues had to operate on each other. One of our doctors died on an improvised operating table, an office desk, while his colleagues tried to save his life," Cone said.

Is U.S. bombing of Afghan hospital a war crime?

A balance between humanity and military necessity

In general terms, a war crime may be committed when there is an attack on a civilian population during an armed conflict, said Steven Kay, a lawyer who defended Kenyan President Uhuru Kenyatta against charges of crimes against humanity at the International Criminal Court,

There is an extensive body of law that regulates military action during conflict.

The aim, said Anthony Dworkin, a human rights expert at the European Council on Foreign Relations, is to draw a balance between what armed forces are justified to do out of military necessity -- which includes causing collateral damage to civilians -- and the principles of humanity.

"Hospitals enjoy a special protected status under international humanitarian law. So, to attack a hospital or medical facility, whether it is a civilian or military installation, is a crime," Kay said.

Saturday wasn't the first time Doctors Without Borders has complained about military action on the Kunduz hospital.

In July, the aid group condemned what it called a "violent incursion by armed members of Afghan Special Forces." The troops allegedly entered the hospital -- which, according to MSF, "has a strict no weapons policy" like its other facilities -- and "physically assaulted three MSF staff members (and arrested) three patients." Those patients were released after an hour.

"Since it opened in 2011, Kunduz Trauma Center has been a place where all patients can receive free medical and surgical care safely," MSF's Director of Operations Dr. Bart Janssens said at the time. "This serious event puts at risk the lives of thousands of people who rely on the center for urgent care."

Collateral damage: A brief history of U.S. mistakes at war