"Frankly, I hope there will be more troop contributions and there needs to be more Afghan forces," Rice told reporters travelling with her on the flight from London.
Rice, speaking against the backdrop of a NATO defence ministers' meeting in Lithuania, said alliance members needed to "come together to give enough military power to do what needs to be done on the front end of the counter-insurgency effort".
After flying into the Afghan capital Kabul, Rice and Miliband travelled in a U.S. military plane to a sprawling base in the southern city of Kandahar, the birthplace of the Taliban and the main city in Afghanistan's most volatile region.
"Kandahar does have an iconic status in the history and position of Afghanistan," said Miliband. "I hope we will be able to take a message in what is really a new drive, a new phase in terms of counter-insurgency."
Rice and Miliband planned to meet NATO commanders in the frontline of the fight against the Taliban.
The United States and Britain have been urging other NATO members to share more of the combat burden in southern Afghanistan where the Taliban insurgency is strongest.
Some NATO countries have bristled at public criticism from Washington over the refusal of a number of alliance members to position their forces in the more dangerous south.
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.
That means most of the fighting against the Taliban is shouldered by Canada, Britain, the United States and the Netherlands. They all want others to contribute more.
Canada has threatened to pull its troops out unless other allies come forward, and Poland's foreign minister has warned against "free-riding" in the alliance.
FIGHT BACK
The Taliban, ousted from power by a U.S.-led invasion in 2001, fought back strongly last year. More than 6,000 people died in fighting in 2007, nearly 2,000 of them civilians.
Rice and Miliband travelled to Afghanistan after holding talks in London on Wednesday.
"We want to spotlight the fact that we and several other allies are standing up and doing the tough job," said a senior U.S. official, who declined to be identified.
Few NATO officials expect major new contributions to be announced during the two-day meeting in Lithuania's capital Vilnius, but Washington wants over coming weeks to extract promises for reinforcements in the south by year-end.
Specifically, the United States wants assurances that allies will fill the gap when some 3,200 U.S. Marines leave the south after a temporary deployment there later this year.
The Taliban have tried and failed to take on NATO forces in direct combat and have largely reverted to a strategy based on suicide and roadside bombings to inflict casualties.
NATO commanders believe the tactic is aimed at gradually sapping the will of European governments to keep troops in the country in the face of popular disquiet over the mission.
Some analysts see the NATO force in Afghanistan as far too small.
"There are no clear indicators that the NATO countries, including the United States, are willing to invest a level of combat forces that would lead to success in southern Afghanistan," said Sean Kay, chair of International Studies at Ohio Wesleyan University.
