The BBC poll showed that most Britons thought the war was "unwinnable"
Scotland's first minister has called on the UK government to consider pulling British troops out of Afghanistan.
Alex Salmond's comments came as a BBC poll suggested 64% of Britons believed the war was "unwinnable".
But Prime Minister Gordon Brown told BBC Scotland the mission was vital in dealing with the threat of terrorism.
Meanwhile, thousands of people across the UK honoured the men and women killed in conflicts past and present with a two-minute silence.
In a poll for the BBC's Politics Show, 42% of the 1,009 adults surveyed said they did not understand the purpose of Britain's mission in Afghanistan.
Some 63% of those surveyed felt UK troops should be withdrawn as soon as possible, and 52% agreed that levels of corruption in Afghanistan's government meant the war was "not worth fighting for".
POLITICS SHOW/COMRES SURVEY
I feel I have a good understanding of the purpose of Britain's mission in Afghanistan
Agree 54%, disagree 42%, don't know 4%
All British forces should be withdrawn from Afghanistan as quickly as possible
Agree 63%, disagree 31%, don't know 6%
The war in Afghanistan is unwinnable
Agree 64%, disagree 27%, don't know 10%
The levels of corruption involved in the recent Presidential election show the war in Afghanistan is not worth fighting for
Agree 52%, disagree 36%, don't know 12%
Sample: 1,009 adults polled by phone on 4 and 5 November
Mr Salmond told BBC Scotland's Politics Show: "I'm not surprised by the findings, because what you've got among the public is a combination of great support for the troops on the ground, as you would expect, but no confidence whatsoever in the government's strategy in pursuing the conflict."
He went on: "There has to be the fundamental reassessment of the role, mission, strategy - nothing should be off the table, that should include the possibility of a withdrawal."
But Mr Brown defended the reasons for having soldiers in Afghanistan, telling BBC Scotland: "It's our duty on every occasion that people ask, as they're entitled to do, the question, 'why are we in Afghanistan and what is the future for our venture in Afghanistan?'
"It's right that we explain there is a chain of terror that links Pakistan and the Afghan-Pakistan border to the streets of our cities in Britain and, if we do not take action in Pakistan and Afghanistan, then al-Qaeda would be plotting more and more chaos in the streets of our country."
Scottish Conservative leader Annabel Goldie said the UK government had to be much clearer about what it expected of the Afghan government, adding: "It is the case that we cannot have our British troops in Afghanistan unclear as to what the ultimate democratic mission is and that's got to be spelled out by the Afghan government."
Former Liberal Democrat leader Charles Kennedy said the objectives at the start of the mission in Afghanistan seemed well-defined and carried broad support.
"The problem has been that, in the intervening years, as the death toll has mounted the objectives have kept changing," he said.