The Russians helped provide information on Afghanistan before and during the war against the Taleban.
He also asked for strong diplomatic pressure on Pakistan, who are the Taleban's strongest international backers.
The rebel Northern Alliance in Afghanistan say the US strikes have crippled the Taleban's fighting ability.
On Tuesday, Mr De Mul left Kabul after several days of talks with Taleban ministers.
Another 1, 500 American soldiers are fighting suspected Taleban and al-Qaeda guerrillas in the south and east of Afghanistan.
Senior American officers have expressed concern that Taleban and al-Qaeda elements may become more active during the spring.
Earlier this week, the Taleban said Pakistan had agreed to sell wheat to Afghanistan to ease food shortages.
There is little sign that sanctions will change the Taleban's policies, or weaken their position within the country.
Regarding former members of the Taleban, Mr Karzai said those who had no criminal record would be freed.
The US also dismissed a Taleban report that they had captured up to 40 US servicemen in Afghanistan.
Most of them were captured in Afghanistan in late 2001 during the US-led invasion to oust the Taleban regime.
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Gen Musharraf said the deal had been struck in order to fight the Taleban, not to have dealings with them.
There are about 18, 000 US-led foreign troops in Afghanistan tracking al-Qaeda and Taleban militants, with security patchy outside the capital Kabul.
There are pupils in these classes who had begun school, but who were stopped from attending lessons under the Taleban regime.
It's likely to take more than one crisis, whatever its outcome, to make any long-term difference in the Taleban's international standing.
Correspondents say there is a growing international debate about whether to negotiate with the Taleban as the insurgents make gains in Afghanistan.
The Taleban's opposition to women receiving an education has meant that many young Afghan females have never received any formal classroom lessons.
The US has said it is sending up to 30, 000 new troops to Afghanistan this year to take on a resurgent Taleban.
The BBC Kabul correspondent says the Taleban appear to be on the run in most of the north and centre of Afghanistan.
On the phone to Mr Blair, Mr Khatami strongly denied what he called baseless rumours that Taleban fugitives had been allowed to cross into Iran.
Though all parties, including the Taleban, would be invited to the proposed Loya Jirga, it's extremely doubtful whether the Taleban leadership would attend.
The UN sanctions which have now been imposed on the country make it even less likely that the Taleban will gain that recognition.
When the former Islamic rulers, the Taleban, banned the internet there were no reliable figures on the number of people online in Afghanistan.
Mr Cook was speaking in response to Sunday newspaper reports that British paras could fight alongside American troops surrounding the Taleban in Kandahar.
But, according to the Tajik news agency Asia-Plus, the alliance has admitted losing control of a key district in the north to the Taleban.
Last week, Mr Karzai appealed to the United Nations General Assembly for more to be done to track down Taleban militants outside Afghanistan's borders.
Mr Holbrooke said, however, that the heart of the threat facing Nato in Afghanistan comes from western Pakistan, where the Taleban have much support.
The capture of Pul-e-Khumri would cut the main north-south road through the centre of Afghanistan, leaving the remaining Taleban forces in the north stranded.
Malala Yousafzai attracted public attention in 2009 when she published a blog telling of her life in Swat, in an area under Taleban control.
Taleban Deputy Minister for Trade, Qari Faizan, met representatives of Pakistan's commerce ministry to discuss a 1965 transit agreement, which allows land routes into Afghanistan.
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