Mr Hague is on a three-day tour of the country to meet Hamid Karzai, the Afghan president, and to visit British troops.
He told the Sun newspaper that Britain had led the way in persuading US President Barack Obama’s government that negotiation was the best potential solution to the conflict.
He admitted that any deal might mean accepting “distasteful things” and could anger military veterans and relatives of the 374 British troops killed in Afghanistan.
However, he said he believed that Britain as a whole was “realistic and practical” enough to accept that ending fighting and starting talks was the best way to safeguard national security.
He told the newspaper: “An eventual settlement of these issues is the ultimate and most desirable way of safeguarding that national security.
“But reconciliation with people who have been in a military conflict can be very distasteful.
“In all these types of situations, you do have to face up to some distasteful things.”
Last night, President Obama told Americans that “the tide of war is receding” as he announced plans to withdraw 33,000 US troops from Afghanistan by September 2012.
In a televised address from the White House, the president tried to conveyed hope to an audience wearied by ten years of conflict in Iraq and Afghanistan that “these long wars will come to a responsible end”.
“Even as there will be dark days ahead in Afghanistan, the light of a secure peace can be seen in the distance,” he said, attempting to draw a curtain across the two wars even though tens of thousands of US troops will remain in the field for several years.
Despite concerns that security gains against the Taliban will be undermined, Mr Obama said “we are starting this drawdown from a position of strength”.
With opposition to the continued US presence in south Asia rising in Congress as well as across the heartland, he said that “at a time of rising debt and hard economic times...it is time to focus on nation building at home”.
Mr Obama said he would bring home 10,000 US troops from Afghanistan by the end of this year and the remainder of the 33,000 “surge” forces by the end of next summer.
Downing Street said the president had spoken to David Cameron, the Prime Minister, before he made the announcement.
Mr Hague has said that Britain will retain a presence in Afghanistan for “many years” after combat troops are withdrawn.
