Opposition to war
Miliband was speaking a day after an opinion poll indicated that most Britons think that the war in Afghanistan cannot be won and that its 9,000 soldiers, who are serving under Nato's International Security and Assistance Force (Isaf), should be brought home.
"Clinton pointed out that it is really the beginning of the renewed effort of the US and its Nato allies to shore up the situation inside Afghanistan, trying to deal with the resurgent Taliban and al-Qaeda and its affiliated groups"
Rosiland Jordan, Al Jazeera's correspondent in Washington
At least 22 British soldiers have been killed in Afghanistan over the last month, as resurgent forces loyal to the Taliban and al-Qaeda continue their push for control over large areas of the country.
Clinton said she held a detailed discussion with Miliband about American and British military efforts in Afghanistan.
She said she has "admiration for the incredible courage and sacrifice of British troops" serving in the country.
Rosiland Jordan, Al Jazeera's correspondent in Washington, said that the meeting between Clinton and Miliband comes as the US calls for Nato member countries to remain committed to the mission in Afghanistan.
"One thing that Clinton kept pointing out is that there is a real need to make certain that whichever government stays in power after the Afghan election on August 20 must be able to fully ramp up its internal security apparatus, with US and UK assistance," she said.
"Clinton pointed out that it is really the beginning of the renewed effort of the US and its Nato allies to shore up the situation inside Afghanistan, trying to deal with the resurgent Taliban and al-Qaeda and its affiliated groups.
"She said there was a situation where they are just starting to get the people in to actually help the Afghan police and military do their work."
The administration of Barack Obama, the US president, in February committed 17,000 extra troops to Afghanistan - supporting 36,000 US troops already serving there - as part of its effort to defeat the Taliban and other armed groups opposing the Afghan government.