The White House hopes that the addition of 30,000 US troops, which will begin almost immediately, combined with the pressure of the new deadline, will spur the government of Hamid Karzai into action.
He continued: "Just as we have done in Iraq, we will execute this transition responsibly, taking into account conditions on the ground. We will continue to advise and assist Afghanistan's fecurity forces to ensure that they can succeed over the long haul.
"But it will be clear to the Afghan government – and, more importantly, to the Afghan people that they will ultimately be responsible for their own country."
The speech came as it was announced that British and American troops in Afghanistan are to launch a major new onslaught against the Taliban within weeks.
Thousands of soldiers will be deployed to "deliver a punch" to insurgents responsible for attacks in Helmand province.
The move is part of President Barack Obama's plans to increase US troop numbers by 30,000 to be announced in a speech to the nation.
He will send 9,000 US marines to fight with British forces in an offensive early in the New Year as the advanced guard of a major surge.
Final preparations for the US marines' departure will begin almost immediately. They are expected to deploy shortly before Christmas for an offensive against Taliban strongholds in the south of the country.
Robert Gibbs, the White House press secretary, said "we're going to get in there quickly" in order to "deliver a punch quickly".