Foreign minister Boerge Brende said his country did not have the capabilities to handle the request by the deadlines given so there was no point in continuing the discussions.
He said the US was looking at other alternatives, but did not give details.
Meanwhile, Syrian government troops have ambushed rebels near the capital Damascus, killing at least 40 opposition fighters, according to state media.
The ambush was part of the military's offensive against rebel strongholds around president Bashar Assad's seat of power.
It came hours after Assad's forces captured the town of Hatitat al Turkomen, south of the city, securing a key route that links the capital with Damascus International Airport.
State-run SANA news agency said 40 rebels were killed in the ambush near the Otaiba area, and that a large arms cache was seized, including anti-tank rockets.
The area is part of a region known as Eastern Ghouta, the scene of a chemical weapons attack in August.