"This alliance will stand united and we will stay in Afghanistan as long as it takes to finish our job," he said.
Obama said that Washington considers the war in Afghanistan as not just a US battle but "a Nato mission as well".
"We both agree that it is absolutely critical that we are successful in dismantling, disrupting, destroying the al-Qaeda network ... We are working actively and diligently to consult with Nato at every step of the way," he said.
Call for troops
The US president has said that he is yet to make a decision on whether to send more troops to Afghanistan.
"I think what the president is doing is the mature and correct thing"
Bruce Riedel, senior fellow, Brookings Institute's Saban Centre for Middle East Policy
General Stanley McChrystal, the senior US and Nato commander in Afghanistan, has said that the military effort risks failure unless more troops are sent to the country as part of a revised strategy.
McChrystal is expected to ask for an additional 30,000 to 40,000 troops for combat operations and training of Afghan forces.
Bruce Riedel, a senior fellow at the Brookings Institute's Saban Centre for Middle East Policy, told Al Jazeera that Obama is considering the current strategy in place before committing to any increase in troops.
"I think what the president is doing is the mature and correct thing – to take a hard look at this. The US embarked on a new strategy earlier this year; it has been six months … [but] I think at the end of the day, the president will decide to send in more troops."
Kai Eide, the United Nations' special representative to Afghanistan, on Tuesday called for more troops to help train Afghan security forces.
"Decisions concerning procurement of equipment or weapons will have to be taken soon – more international troops for training and for mentoring will be required," he said.
Eide said that 2009 had been the deadliest year for Afghan civilians in the eight-year war between the US-Nato alliance and fighters loyal to the Taliban and al-Qaeda.
The apparent move by McChrystal to get more US troops sent to Afghanistan comes amid a dramatic rise in the number of US military deaths in the country.
Support among the US public for the mission has dropped in recent weeks, while some Democrats say they are reluctant to support the sending of more soldiers.
Some senior Democrats, including Robert Gates, the US defence secretary, have said that having too large a US military force in Afghanistan runs the risk of it being seen as an occupation force by Afghan civilians.