A statement from his office said the president expressed "deep sorrow for the loss of our compatriots" and "emphasised that innocent civilians must not be killed or wounded during military operations".
The White House and Nato Secretary General Anders Fogh Rasmussen both stressed there would be a full investigation.
White House spokesman Robert Gibbs said: "Obviously, any time there is loss of life in a conflict like this, particularly the civilian loss of life, it's something we've expressed in the past and continue to express great concern about."
Chris Morris, BBC News, Afghanistan
If it emerges that a number of civilians have been killed then that will obviously be very disappointing to Nato.
The issue of civilian casualties caused by international military action is extremely sensitive here. It has caused great anger.
It is something military commanders have said they are determined to clamp down on, because they say if they win territory and not the people then they are not doing their job.
Mr Rasmussen said that although a number of Taliban were killed in the Kunduz incident, there was the possibility of civilian casualties.
He said: "Civilian casualties caused by Isaf are down over 95% from last year's levels. But, as we all know, in conflicts like these, mistakes can happen. In this case, let us now see what the investigation concludes."
European governments also expressed concern at the scale of the civilian casualties and urged a prompt investigation.
British Foreign Secretary David Miliband said Nato needed the commitment of the Afghan people for its mission, adding: "Obviously incidents like this undermine that.
"That's why it's important that we are open and clear about what happened and make sure it does not happen again."
The Kunduz incident follows recent new guidelines issued by the head of international troops in Afghanistan, Gen Stanley McChrystal, saying that much more needed to be done to avoid civilian casualties.
RECENT MAJOR ATTACKS
2 Sep: Blast in Laghman province kills Afghan deputy chief of intelligence and 21 others
25 Aug: Car bomb in southern city of Kandahar kills at least 40
18 Aug: Nine Afghans and a Nato soldier die and more than 50 are injured in Kabul
15 Aug: Bomb outside Nato HQ in Kabul kills seven and injures 90
13 Aug: Twin blasts in Helmand and Kandahar kill 14, including several children
6 Aug: Five American and three UK soldiers, five civilians and five policemen killed by roadside bombs mainly in Helmand
The number of those killed in the Kunduz strike is still not confirmed, with reports varying from 56 to 90.
The reports of the number of militants and civilians killed also varies.
Pictures from Kunduz showed members of the local community preparing some of those who died for burial, while others showed images of the injured being treated in hospitals.
The Nato attack occurred about 7km (four miles) south-west of Kunduz city at about 0200 on Friday (2130 Thursday GMT), 40 minutes after German and Afghan forces called in an air strike.
They reported the two tankers had been hijacked by insurgents as they travelled from Tajikistan to supply Nato forces in Kabul.
One of the drivers of the tankers told the BBC that two of his colleagues had been beheaded when the Taliban carried out the hijacking.
Witness Mohammad Daud, 32, told AFP the militants had been trying to transport the tankers across a river to villages in Angorbagh.
"They managed to take one of the tankers over the river. The second got stuck."
Locals in Kunduz prepare the dead for burial after the air strike
The insurgents apparently opened valves to lighten the load and called in villages to help themselves to fuel.
At this point, the Nato air strike hit the tankers. Nato insists its commanders believed only militants were present.
When day broke, clothing, shoes, jerry cans and other debris could be seen strewn around the two stricken tankers.
Mr Daud said: "Everyone around the fuel tankers died. Nobody was in one piece. Hands, legs and body parts were scattered everywhere."
International Security Assistance Force (Isaf) spokesman Brig Gen Eric Tremblay was later quoted by Reuters as saying: "It would appear that many civilian casualties are being evacuated and treated in the local hospitals.
The air strike came shortly before UK Prime Minister Gordon Brown delivered a key speech defending the Afghan strategy.
He said the aims of Britain and its allies there were "realistic and achievable".
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.