Most people in the UK oppose British military operations in Afghanistan, a survey conducted for the BBC suggests.
There are nearly 5,000 British soldiers in Afghanistan at present
Only 31% support the decision to deploy 5,000 troops to fight the Taleban, while 53% of the population are against the move, according to the ICM poll.
Nato is extending its mission to cover the whole of the insurgency-hit nation.
Meanwhile Defence Secretary Des Browne has rebuffed reports that commanders wanted soldiers withdrawn from Iraq to bolster the UK presence in Afghanistan.
"My view, and military commanders share this view, is that we have a vital job to do in Iraq. We have a responsibility to the Iraqi people.
"There is no division between us and military commanders about what we are doing at the moment," Mr Browne told BBC Radio 4's The World at One.
Currently Britain has nearly 5,000 troops in Afghanistan - including 3,600 in the violent Helmand province - with a further 900 on the way.
A separate development will see the 12,000 US troops involved in Operation Enduring Freedom - a mission in Afghanistan which is separate to the Nato deployment - coming under Nato control.
UK TROOPS IN AFGHANISTAN
53% oppose British military operations
31% support the UK's presence
63% think troops are helping to battle the Taleban
71% believe soldiers are part of the fight against al-Qaeda
46% claim the military is trying to stop the flow of drugs
Source: ICM poll for the PM programme on BBC Radio 4
The decision will give the alliance a total of 32,000 soldiers.
Asked why British troops were fighting in Afghanistan, 63% said it was to help the Afghan government fight the Taleban.
Some 71% believed it was part of the international fight against al-Qaeda, while 46% thought they were focusing on cutting the supply of drugs from the country.
Mr Browne said he believed support for British military operations would increase "as we begin to see the results and improvements" of spreading the Nato force to all areas of Afghanistan.
'Spike of activity'
Conservative MP Mark Lancaster, a Territorial Army reservist who was called up to serve as a Royal Engineer for a two-month spell in Afghanistan, said the recent focus of the media had been on the "spike of activity" in Helmand.
"There's been very little coverage in the media of the reconstruction and development side," he told the PM programme on BBC Radio 4.
"Progress is being made, but it's slow."
He also thought British forces were going to be in Afghanistan for "a very long time" and there should be "some political honesty on that".
But Nato secretary general Jaap de Hoop Scheffer warned that the mission in Afghanistan cannot be allowed to fail.
"Do please realise the consequences of Nato not being there, Nato failing and Afghanistan becoming the black hole, the hotbed for terrorism training and human rights abuses.
"The consequences of such a situation would be felt in London," he told The World at One, "because it [Afghanistan] would again be a nation which was exporting terrorism.
"We have to stay the course - we will stay the course and we will prevail."
The poll, commissioned by PM, saw 1,011 adults questioned over the past two days.