When asked what would happen if other Nato countries failed to contribute, she added: "In the final analysis, you will see more troop contributions."
Britain's Miliband said international efforts to stabilise Afghanistan were entering a "new phase" which combined military solutions with political and developmental concerns.
Zeina Khodr, Al Jazeera's correspondent in Afghanistan, said Rice and Miliband could be aiming to reassure the Afghan government that Nato remains committed to its mission in the country.
"Nato has been divided - the US wants their allies to deploy more troops in Afghanistan [and] to deploy them in areas where there has been a lot more violence, particularly in the south and in the west," she reported.
The Nato-led International Security Assistance Force has 43,250 troops in Afghanistan. The US has a further 14,000-plus troops outside the Nato force.
A country-wise breakdown:
US: 15,000 troops (mainly east)
UK: 7,800 (mainly south)
Germany: 3,210 (north)
Italy: 2,880 (west and Kabul)
Canada: 2,500 (south)
The Netherlands: 1,650 (south)
France: 1,515 (Kabul)
Poland: 1,100 (mobile)
Australia: 1,070 (south)
Other countries: Denmark (780); Spain (740); Turkey (675); Romania (535)
"Other observers tell us that the Americans would like to bridge the gap between the Afghan and British governments, as ... Hamid Karzai [Afghan president] has openly criticised the British in the past, particularly their policies in Helmand province in the south."
Most of the fighting against the Taliban is currently shouldered by Britain, the United States, Canada and the Netherlands.
Last week, Germany publicly rejected US calls to deploy more troops in the battle scarred south.
Under its parliamentary mandate, Germany can send only 3,500 soldiers to the less dangerous north.
Rice also told reporters that Robert Gates, the US defence secretary, will be working on building troop contributions at a Nato meeting of defence ministers in Vilnius, Lithuania,
The Nato-led International Security Assistance Force (Isaf) comprises some 42,000 troops from 39 countries.
Commanders in Afghanistan have been calling for an extra 7,500 troops to battle the Taliban stronghold in the south.