"After years of substantial investments by the American people, governance in Afghanistan must improve in a reasonable period of time to ensure a successful transition to our Afghan partner," the official said, adding that Obama had yet to decide on proposals for increased troop deployments.
The meeting reportedly focused on four possible options for a revised US strategy, and how long each would take to implement.
The talks come about three months since General Stanley McChrystal, the senior US military commander in Afghanistan, requested thousands of additional troops.
At the same time, US public opinion is growing increasingly sceptical about the conduct and objectives of the eight-year-old war, with support waning as combat deaths hit record levels.
On Wednesday, a new opinion poll showed a growing number of Americans believe the war in Afghanistan is not going well and disapprove of Obama's handling of the situation.
The survey by the Pew Research Centre showed 57 per cent now say the military effort in Afghanistan is going either not too well or not well at all, up from 45 per cent in January.
Also on Wednesday, reports emerged in US media that the US ambassador to Afghanistan has expressed his own strong reservations over an increased troop deployment.
According to the New York Times and Washington Post, Karl Eikenberry, writing in classified cables to top US officials, expressed worries over the Afghan administration and its ability to tackle widespread corruption that has spurred the Taliban's revival.
In addition, Eikenberry was quoted as saying that additional troop deployments would only increase Afghanistan's reliance on US security forces. He also raised concerns over what he called the erratic behaviour of Hamid Karzai, the Afghan president.
Eikenberry reportedly attended Wednesday's war cabinet meeting by video link from Kabul.
Peter Galbraith, a former UN diplomat in Afghanistan, said that he also believed it was wrong to send more troops following the controversial presidential election.
"It is a mistake. I don't think they can accomplish the mission that they are being given because they have no credible local partner to work with," he told Al Jazeera.
McChrystal has said he needs at least 40,000 extra troops to avoid failure in the conflict, but it is not clear what level of deployment Obama favours.
The US currently has nearly 68,000 troops deployed to fight a resurgent Taliban and al-Qaeda in Afghanistan. As Obama debates a revised strategy in the eight-year war, officials say he is considering four options.
One option is the request put forward by the top US commander in Afghanistan, General Stanley McChrystal, for 40,000 more troops to secure the towns and cities.
Another option, said to be carrying the most favour among officials, is an increase of 30,000. Washington could then try to convince Nato allies to contribute, bringing the number of troops to the 40,000 McChrystal recommended.
Options three and four include significantly lower troop deployments, from 20,000 to 15,000, most of whom would serve as trainers for the Afghan security forces.
Critics have accused the US president of dithering over the issue, but Obama has said he will not rush a decision to put more US personnel in harm's way.
Speaking before the White House meeting, General David Petraeus, commander of the US Central Command, told the CNN news channel that a decision on a revised US strategy was near after months of deliberation.
Obama left the US on Thursday for a nine-day tour of Asia and is not expected to announce a decision until after his return to Washington.
According to The New York Times, the four options under consideration include McChrystal's proposal, which would significantly ramp up the US presence in Afghanistan.
There are currently nearly 68,000 US troops in Afghanistan, along with 40,000 other allied forces.
Credibility in question
The debate over the US commitment to Afghanistan comes against mounting concerns in Washington over the credibility of Karzai's government after the recent fraud-marred election.
Hillary Clinton, the US secretary of state, said on Thursday that she was concerned about "corruption, lack of transparency, poor governance [and] absence of the rule of law".
"We're looking to President Karzai as he forms a new government to take action that will demonstrate - not just to the international community but first and foremost to his own people - that his second term will respond the needs that are so manifest," she said in the Philippines.
Rampant corruption has been seen as undermining allied efforts to stabilise Afghanistan, where a Taliban-driven insurgency has swelled over the past year.
"The culture of self-interest should be top priority," Shukria Barakzai, a member of the Afghan parliament, said.
"I think right now, for the first time the people of Afghanistan, Karzai himself and the international community have got one common issue - action against corruption," she told Al Jazeera.