Fighting in Afghanistan could be stopped "in weeks" if Pakistan told the Taliban to end the insurgency, the head of the Afghan army has told the BBC. Gen Sher Mohammad Karimi said Pakistan controlled and gave shelter to Taliban leaders, deliberately unleashing fighters on Afghanistan. Pakistan denies controlling the militant group. It was one of the Taliban's main supporters from its launch in 1994 until the 2001 fall of the regime. Most of the Taliban's leaders reportedly then fled to Pakistan and the group is still considered to be heavily dependent on the support of certain elements in the country. Sensitive time "The Taliban are under [Pakistan's] control - the leadership is in Pakistan," Gen Karimi told the BBC's Today programme. "Madrassas have been closed and all the Taliban have been unleashed to Afghanistan." Afghanistan could achieve peace if this was desired by both the US and Pakistan, said the general. Gen Karimi's comments come at a sensitive time "If [Pakistan] put pressure on [Taliban] leadership or convinced them what to be done, that can help a lot," he added. A Nato report leaked in April said Pakistan was aware that Taliban leaders were taking refuge within its borders. Senior Taliban figures such as Nasiruddin Haqqani were housed close to ISI headquarters in Islamabad, added the report, entitled State of the Taliban. It was based on the interrogations of 27,000 captured Taliban, al-Qaeda and foreign fighters as well as civilians. But Pakistan consistently denies wielding influence over the Taliban, saying many militants have based themselves across the border in Afghanistan's eastern province of Kunar, from where they are known to have carried out attacks in north-western Pakistan. Securing the long, porous border between the two countries has long posed a major challenge to the authorities. Lack of trust Gen Karimi's comments come at a sensitive time, says the BBC's Richard Galpin in Islamabad. The US is pushing for peace talks with the Taliban as Nato combat troops continue to withdraw from Afghanistan - a process due to be completed next year. Last month the Taliban opened their first official overseas office in the Qatari capital, Doha - the first step ahead of the expected peace talks. US and Afghan leaders want the Taliban to join the Afghan government as a result of the peace process. They say peace talks will succeed when the Taliban finally sever all ties with al-Qaeda, end violence and accept the Afghan constitution, including its protections for women and minorities. Pakistani officials have been involved in the background talks, and generally say Islamabad wants a "friendly, peaceful and sovereign" Afghanistan. But they are adamant that Pakistan's "legitimate interests" in Afghanistan must be recognised after the withdrawal of Nato troops. Within hours of the opening of the Doha office, however, Afghan President Hamid Karzai raised concerns about the process not being Afghan-led and suspended plans for Afghan officials to meet the Taliban. For their part, the Islamist militants said they did not trust the Afghan government and considered it a "puppet" of the US. The Taliban insist on the complete withdrawal of foreign forces as a pre-condition to becoming part of a political settlement in Afghanistan. Although Nato's combat troops are due to leave the country by the end of 2014, the US plans to station forces after that as part of a bilateral security agreement. Details are still to be agreed by Kabul and Washington. BBC News - Afghan army chief: 'Pakistan controls Taliban'