The US has said after its formal draw-down of troops from Afghanistan by the end of the year, it could leave as many as 8000 for counter-terrorism operations against al Qaeda targets and to train Afghan forces.
But Mr Karzai's refusal to sign a security deal has frustrated the White House, which has been forced to abandon an earlier demand he sign the deal in weeks, not months. The White House said in a statement: "Specifically, President Obama has asked the Pentagon to ensure it has adequate plans in place to accomplish an orderly withdrawal by the end of the year should the US not keep any troops in Afghanistan after 2014."
Mr Obama told Mr Karzai in a phone call that he had given the order to the Pentagon, the first substantive discussion between the two leaders since June.
A senior government official from neighbouring Pakistan predicted dire consequences should the US withdraw completely.
He said: "In my opinion, zero option should not be an option. In my opinion, zero option means civil war in Afghanistan," the official told reporters in Washington.
Nato officials had been playing down the delay in Mr Karzai signing the security agreement.