The Liberal and Christian Democratic parties joined forces to make the demand, which has the backing of the Labour and Socialist Left Parties.
"We demand a complete review of all our missions in Afghanistan. What has worked well, what has worked badly and what we can learn from it," Liberal leader Trine Skei Grande told Dagsavisen newspaper.
The call followed the admission by Norway's defense minister Ine Marie Eriksen Søreide on Sunday that Norwegian troops would continue to operate in Afghanistan for years after 2014, when the Nato-led International Security Assistance Force (ISAF) is scheduled to be replaced by a smaller training and mentoring mission.
After visiting Afghanistan to review the troops, Søreide said that the end of ISAF would not mean a lesser role for Norwegian troops.
“I don’t see that it’s very likely that we will contribute with something completely different from today,” she told news bureau NTB.
Both the Christian Democratic and Liberal Parties support reducing the Norwegian involvement in the new Nato operation, Labour largely supports maintaining Norwegian troops, and the Socialist Left support a total withdrawal as soon as possible.