By Sue Pleming
Rice, speaking en route to London where she will discuss strategy on Afghanistan with British leaders, called for the quick appointment of an envoy to coordinate what she termed NATO's bumpy mission.
"We believe very strongly that there ought to be a sharing of that burden throughout the (NATO) alliance," said Rice, adding she did not wish to denigrate the contribution of allies.
Germany, for example, under its parliamentary mandate can send only 3,500 soldiers to the less dangerous north as part of the 42,000-strong NATO mission.
The Taliban, ousted from power by a U.S.-led invasion in 2001, fought back strongly last year.
Western efforts in Afghanistan have been fragmented and Rice said she hoped a new international envoy could be appointed soon to coordinate this work.
"We want to be very clear that this is a sovereign Afghan government and it has to take its own decisions, but it has a heavy reliance on international support," said Rice.
Rice, due to meet Prime Minister Gordon Brown and Foreign Secretary David Miliband, said she believed another European was likely to get the post.
"It is bumpy and there is a lot of maturing that the alliance is having to do ... Frankly, counter-insurgency is really hard for any traditional military, let alone (NATO)," said Rice.
Canada has said it would pull out its forces early next year if other NATO countries did not send in more.
Asked for her assessment, Rice said there were "challenges" and that the Taliban had "by no means been defeated".
