But Khurshid Kasuri, Pakistan's foreign minister, said: "I am certain that, where Mullah Omar is concerned, he is Afghanistan. Why should he be in Pakistan?
"... he would not be a very wise man to be in Quetta ... it is crawling with agents so I don't think that is correct."
"Having security is of no use unless a massive amount of aid is invested in the community"
Justtone, Nottingham, UK
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James Bays, Al Jazeera's correspondent in Kabul, said that a senior adviser to the foreign minister had told him that the Afghan government had informed Pakistan, the United States and Nato of their information about Mullah Omar's whereabouts, but nothing had been done.
"He [the adviser] made the allegation ... that they believe that Mullah Omar has been in the custody, or at least under the hospitality as he described it, of the Pakistani intelligence service, the ISI, for five-and-a-half years now and no one is doing anything," Bays said.
Mullah Omar led the Taliban government in Afghanistan from 1996 until it was overthrown by a US-led invasion in 2001, launched after it failed to hand over al-Qaeda leaders wanted for the September 11 attacks.
Earlier this year, Abdelhaq Hattiq, a Taliban spokesman arrested by Afghan government forces, also alleged that Mullah Omar was living in Quetta.
Karzai has also blamed Islamabad for a resurgence of violence along their common border.
"We have almost daily reports of suicide bombers coming from there," he told the newspaper. "If we have better co-operation from Pakistan, a great many of these cross-border crossings would stop."
Kamal Hyder, Al Jazeera's correspondent in Islamabad, said; "For people in Pakistan, Karzai's song remains the same.
"People will tell you he has been accusing Pakistan for months now and they've also been saying perhaps it is because Karzai has been unable to rein-in his own country."
The Taliban has gathered strength over the last year, carrying out near-daily attacks in the south and east of the country despite an increase in the number of Nato-led troops.
Karzai has put this down to the decision to fight the Taliban in Afghanistan, rather than targeting the group's leadership and financial backing in Pakistan.
Afghan and Pakistani frequently trade allegations about each others efforts in tackling the Taliban fighters which operate along the porous border.
The two countries recently clashed over Islamabad's plan to place mines and a fence along the 2,000km-long border.
Source: Al Jazeera and agencies