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Citing a communique which it said will end Thursday's meeting in London, the Times said Afghan forces up will be given up to half a decade to take responsibility for "physical security".
Continued support from Western troops will be needed until then.
The draft statement commits the Afghan troops to "taking the lead and conducting the majority of operations in the insecure areas of Afghanistan within three years and taking responsibility for physical security within five years", according to the paper.
Some of the more stable regions could come under the control of Afghan security forces at the end of this year or early 2011 with support from Western troops, "providing conditions are met", the document adds.
The Ministry of Defence in Britain, which has the second biggest contingent of troops in Afghanistan after the United States, said Monday it did not comment on leaked documents.
But it added a decision on pulling out troops would be based on "conditions, not arbitrary timelines."
More than 113,000 international troops are fighting the Taliban under US and NATO command and losing soldiers almost daily, in the conflict which started with the US-led invasion of 2001.
The United States is pouring another 30,000 troops into Afghanistan this year, on top of more than 70,000 already there, but under US President Barack Obama's plans they are begin withdrawing in July 2011.
Details of a Western-funded reconciliation plan to use offers of cash and jobs to tempt insurgents away from the Taliban will also form part of the closing statement, the Times said, a scheme unveiled several days ago by Afghan President Hamid Karzai.
Britain's foreign ministry, which is organising the conference, also said it did not comment on leaked documents.
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