Speaking in London on February 6 before leaving for Kabul, Rice said the public in NATO member states must realize that the fight for Afghanistan is no peace-keeping mission, but rather a long-term battle.
She said the NATO alliance is facing "a real test" in its campaign to rid Afghanistan of Taliban insurgents, Reuters reported.
Her comments come amid increasingly strong demands from the United States and other NATO front-line countries for more combat troops and equipment from their fellow alliance members.
Miliband, also speaking in London ahead of their trip, welcomed Rice's comments, and assured her that Britain shared Washington's concerns.
"We welcome the attention that's been given to the situation in Afghanistan over the last few weeks," Miliband said. "The challenges there are very large, and it's because the challenges are large that we are so committed to being there. Both of our countries are committed to our work in Afghanistan for the long term."
Later, Rice and Miliband flew together to Afghanistan, where on February 7 they inspected the front-line areas around the southern city of Kandahar. Their visit was meant as a morale booster and as a familiarization trip.
Back in Kabul, they were to meet Afghan President Hamid Karzai, in what is being seen as a bid to thaw a frost in British-Afghan relations.
Karzai has blamed the British army for some of the violence in the south, saying the British sacked all the local leaders in areas under their control, contributing to the volatile security situation there.
Karzai is also angry at alleged British efforts to get Taliban fighters to defect, an undercover activity that he said he did not authorize.
The visiting top U.S. and British diplomats are also expected to use their visit to reassure Afghans of their commitment to improving the civil and economic infrastructure of the country, as a nonmilitary means of undercutting the Taliban.
"We're committed to bringing together the economic, social, and military aspects of our work," Miliband said in London on February 6. "We're committed to active support of the Afghan government as it strives to build a decent society in that very poor country. And we're committed to rallying an international alliance of many countries to effectively support the Afghan government."
A wave of recent independent reports has highlighted the urgency for the West and the Kabul government to make progress against the resurgent Taliban.
Last month, the U.S. Afghanistan Study Group, headed by Ambassador Thomas Pickering and General James Jones, released a report warning of a serious threat of resurgent violence and the real prospect of a "failed or failing state."