intensive care after she was shot in the head on a school bus on Tuesday, an assassination attempt that has appalled Pakistan.
It took place in Mingora, the main town of the Swat valley in Pakistan's northwest, where Malala had campaigned for the right to an education during a two-year Taliban insurgency which the army said it had crushed in 2009.
On Wednesday doctors successfully performed a three-hour operation to remove a bullet lodged near her shoulder, where it moved after entering her head, in a military hospital in the northwestern city of Peshawar.
Preparations were made to fly her abroad, but a military source told AFP she was currently too ill to travel. White House spokesman Jay Carney said US forces were ready to offer transport and treatment to the teenager if needed.
Obama believed the shooting was "reprehensible and disgusting and tragic", Carney said.
"Directing violence at children is barbaric, it's cowardly, and our hearts go out to her and the others who were wounded as well as their families."
Malala won international recognition for highlighting Taliban atrocities in Swat with a blog for the BBC three years ago, when the Islamist militants burned girls' schools and terrorised the valley before the army intervened.
Her struggle resonated with tens of thousands of girls denied an education by Islamist militants across northwest Pakistan, where the government has been fighting local Taliban since 2007.
Ban's spokesman said the UN chief was "deeply moved" by Malala's campaign for education rights and called for "the perpetrators of this heinous and cowardly act to be swiftly brought to justice".
The provincial government announced a 10 million rupee ($104,000) reward for information leading to the capture of Malala's attackers.
The attack has drawn condemnation from around the world and highlighted the enduring presence of Taliban extremists in the scenic Swat valley, which Pakistan's government has been trying to restore as a tourist destination.
"It happened in broad daylight. It means some (extremist) elements are still here and it is really disturbing for us," said Habibullah Khan, a shopkeeper in the Mingora bazaar.
Powerful army chief General Ashfaq Kayani visited Malala on Wednesday and said it was time to "further unite and stand up to fight the propagators of such barbaric mindset and their sympathisers".
Schoolchildren across the country on Wednesday offered prayers for Malala's recovery, but the Pakistani Taliban have issued a statement saying that any female who opposes them should be killed.
Malala's uncle Saeed Ramzan, citing her doctors, said she was stable after the lengthy operation to remove the bullet.
"But they said the next 48 hours are important and after that it will be decided whether she will be sent abroad or not," he told AFP at the family home in Mingora, which is under heavy police guard.
"We saw movement in her body today but she is still unconscious."
Interior minister Rehman Malik said she would remain in Peshawar until medics agreed she could be moved, with Dubai cited as a possible destination for further treatment.
Taliban bombers have killed thousands of Pakistani soldiers and civilians over the past five years, but many in the country blame the United States and its 2001 invasion of neighbouring Afghanistan for the violence.