(CNN) President Barack Obama has personally apologized. But he didn't go far enough, according to Doctors Without Borders, the aid group whose hospital in the Afghan city of Kunduz was hit by a deadly U.S. airstrike.

The charity group -- which is also known as Medecins Sans Frontieres, or MSF, and provides medical care in some of the world's most dangerous places -- is calling the strike an "attack on the Geneva Conventions" and urging an independent investigation by a never-before-used international commission.

The International Humanitarian Fact-Finding Commission has been in existence since 1991. It requires a request by one of the 76 nations that have signed on to it for it to begin its work. Its job is to investigate whether international humanitarian law has been violated.

"Governments up to now have been too polite or afraid to set a precedent," Dr. Joanne Liu, president of Doctors Without Borders, said Wednesday. "The tool exists, and it is time it is activated."

On Wednesday morning, Obama called and apologized directly to Liu. In a White House statement on that conversation, he highlighted a U.S. military investigation into the strike and pledged full support to a joint NATO and Afghan government probe.

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.

'If we let this go, we are basically giving blank check to any countries at war' says #MSF Int'l Prez @JoanneLiu_MSF pic.twitter.com/p3YDpUepbq — MSF East Africa (@MSFNairobi) October 7, 2015

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.

What the U.S. said and when Saturday, 3 October -- Col. Brian Tribus, spokesman for U.S. Forces in Afghanistan "U.S. forces conducted an airstrike in Kunduz city at 2:15am (local), Oct 3, against individuals threatening the force. The strike may have resulted in collateral damage to a nearby medical facility. This incident is under investigation." Sunday, 4 October -- Gen. John Campbell, U.S. military chief in Afghanistan "U.S. forces conducted an airstrike in Kunduz city at 2:15am (local), Oct 3, against insurgents who were directly firing upon U.S. service members advising and assisting Afghan Security Forces in the city of Kunduz. The strike was conducted in the vicinity of a Doctors Without Borders medical facility." Monday, 5 October -- Gen. John Campbell, U.S. military chief in Afghanistan "We have now learned that on October 3, Afghan forces advised that they were taking fire from enemy positions and asked for air support from U.S. forces. An airstrike was then called to eliminate the Taliban threat and several civilians were accidentally struck. This is different from the initial reports, which indicated that U.S. forces were threatened and that the airstrike was called on their behalf." Tuesday, 6 October -- Gen. John Campbell to the Senate committee "On Saturday morning our forces provided close air support to Afghan forces at their request. To be clear the decision to provide aerial fires was a U.S. decision, made within the U.S. chain of command. A hospital was mistakenly struck. We would never intentionally target a protected medical facility ... I assure you that the investigation will be thorough, objective and transparent."

'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.

A balance between humanity and military necessity

Photos: Doctors Without Borders hospital attacked in Afghanistan Photos: Doctors Without Borders hospital attacked in Afghanistan Flames are visible inside a Doctors Without Borders hospital in Kunduz, Afghanistan, after a U.S. airstrike on Saturday, October 3. At least 30 people died in the attack, the charity said in its internal review of the strike released Thursday, November 5. The commander of U.S. forces in Afghanistan has said the hospital was hit accidentally. Hide Caption 1 of 5 Photos: Doctors Without Borders hospital attacked in Afghanistan Doctors Without Borders said it had emailed the GPS coordinates of its main hospital and administration office building at the Kunduz center before the airstrike. The U.S. commander said airstrikes were called after Afghan troops advised they were "taking fire from enemy positions."

Hide Caption 2 of 5 Photos: Doctors Without Borders hospital attacked in Afghanistan Doctors Without Borders is asking for an indepedent investigation by the International Humanitarian Fact-Finding Commission. President Barack Obama has apologized to the charity group for the attack. Hide Caption 3 of 5 Photos: Doctors Without Borders hospital attacked in Afghanistan The attacks came as fighting intensified between Afghan government forces -- supported by U.S. air power and military advisers -- and the Taliban, which invaded Kunduz in late September. Hide Caption 4 of 5 Photos: Doctors Without Borders hospital attacked in Afghanistan "We were running a hospital treating patients, including wounded combatants from both sides -- this was not a 'Taliban base,' " said Dr. Joanne Liu, international president of Doctors Without Borders or Médecins Sans Frontières, upon release of the group's internal review of the attack. Hide Caption 5 of 5

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."