White House Press Secretary Josh Earnest said that Obama called MSF chief Joanne Liu "to apologise and express his condolences" over the weekend attack.
"President Obama spoke by telephone with Doctors Without Borders International President Dr Joanne Liu, to apologise and express his condolences for the MSF staff and patients who were killed and injured when a US military air strike mistakenly struck an MSF field hospital in Kunduz, Afghanistan over the weekend," Earnest told reporters.
Obama told her that the US, if necessary, would make changes that would make tragedies like this one less likely.
MSF, which has condemned the attack as a war crime, has demanded an international probe into the attack that killed at least 22 people, including women and children, after reports said NATO's top regional commander thought US forces broke rules of engagement.
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The medical charity's demand came a day after General John Campbell, the top US and NATO commander in Afghanistan, said the "hospital was mistakenly struck."
Campbell's admission was the latest in a series of shifting accounts the Americans have offered for the strike, which have ranged from dubbing the bombing "collateral damage" to saying it was carried out to protect American troops.
Three separate investigations -- by the US military, NATO and Afghan officials -- are underway into the deadly strike on Saturday.
Earnest said Obama also spoke with Afghan President Ashraf Ghani and pledged to keep working closely with his government.
"After completing that call, the President telephoned Afghan President Ashraf Ghani to express his condolences for the innocent loss of life in that incident," he said.
"...When we make a mistake, we're honest about it, we own up to it, we apologise where necessary, as the president did in this case and we implement the kinds of changes that make it less likely that those kinds of mistakes will occur in the future," Earnest said.