Mr Rasmussen said: “If we were to walk away and turn our backs on Afghanistan, al Qaida would be back in a flash.
They would have a sanctuary from which to launch their strategy of global jihad, a strategy that is directed first and foremost against us.
Speaking to the same conference, David Miliband, the Foreign Secretary, said that British troops are fighting in Afghanistan not to defeat Taliban insurgents but to persuade them to lay down their arms and enter politics. Britain’s goal in Afghanistan is “not a fight to the death” but a political settlement, he said.
Mr Rasmussen's intervention came as it emerged that a British soldier shot dead in Afghanistan on Sunday had complained before his death that new body armour had not been delivered.
Rifleman Andrew Fentiman, 23, a Territorial Army soldier from Cambridge, wrote on the internet two weeks ago: "We are still waiting on these new body armour and helmets that were promised to us."
A total of 234 British service personnel have died in Afghanistan since 2001, and public support for the 9,000-strong British mission there is flagging.
To reassure wavering voters, the Prime Minister has begun to talk up the prospect of an exit from Afghanistan. On Monday, he proposed an international summit on Afghanistan that will set out a “timetable” for handing territory back to the Afghans starting next year.
Mr Rasmussen backed that schedule, “where conditions permit”.
However, Lord Robertson, a former Labour defence secretary, warned the Prime Minster not to be pushed into an early exit from Afghanistan, saying leaving too quickly would raise the terror threat to the West.
He said: “Our people will never forgive this political generation if we were to walk away from the threat and horrors that we know would be the consequences of prematurely getting out of Afghanistan.”
The Prime Minister’s new emphasis on a timetable for exit has also caused private concern among British commanders, who worry that any sign that Britain’s commitment to the Afghan mission is waning will encourage the Taliban.
David Richards, the Chief of the General Staff, has said that it could be another five years before British troop numbers fall.