The claim by Mohammad Hanif, a Taliban spokesman being held in Afghanistan, appears to be the first time a Taliban member has said Omar is in Pakistan and not leading fighting in Afghanistan.
Shaukat Sultan, a Pakistani military spokesman, said on Thursday: "This is as absolutely absurd and ridiculous a statement that one could have."
Afghan officials have often said they believe Omar and other Taliban leaders are living in Pakistan.
Güncelleme Tarihi: 20 Eylül 2018, 18:16
Afghan and US military officials have also previously said in private that they believe members of Pakistan's Inter Services Intelligence (ISI) agency are helping the fighters.
John Negroponte, the US intelligence chief, said last week that al-Qaeda leaders were hiding out in Pakistan and it would be necessary to eliminate Taliban safe havens in Pakistan's tribal areas to end the Afghan unrest.
The Afghan government said on Tuesday that authorities had arrested Hanif, who was also an aide to Omar, along with two other men the previous day after they crossed into Afghanistan from Pakistan.
In a video recording of part of his interrogation released by Afghan authorities, Hanif said Omar was living in the Pakistani city Quetta under the protection of the ISI.
He also said Hamid Gul, the former ISI chief, was organising the training of suicide bombers at a religious school in Pakistan.
Speaking of Hanif's video evidence, Sultan said: "It appears that it has been given under coercion and we outrightly reject it."
He said Afghanistan should have provided evidence to Pakistani authorities.
Gul, ISI chief during the 1980s when the agency helped organise Afghan opposition to the Soviet invasion of their country, also dismissed Hanif's statement, saying: "This is absolutely nonsense. The same thing appeared some time back in the New York Times, my name was mentioned. It's a rehash of the same story."
Referring to Hanif, Gul said: "I don't know who he is. It's totally wrong."
Afghan suspicion of Pakistani support for the Taliban has seriously strained relations between the neighbours as the anti-government campaign intensified over the past year.
Pakistan was the main backer of the Taliban during the 1990s but officially stopped helping them after the September 11, 2001, attacks, when it joined the US' so-called "war on terrorism".
A UN official in Afghanistan this month called on Pakistan to do more to tackle Taliban leaders in Quetta.