Mullah Baradar was seized in a secret joint operation by the US and Pakistan in Karachi several days ago, the New York Times reported late on Monday.
Senior US officials have confirmed the report.
"This operation was an enormous success," one told ABC News. "It is a very big deal."
However, a Taliban spokesman told the AFP news agency on Tuesday that the reports were "all untrue".
"[Baradar] is currently in Afghanistan, where he is leading all jihadi activities," said Yousuf Ahmadi. "He is here with us and is in contact with us."
This claim is "not credible," says correspondent Behroz Khan from Peshawar in north-west Pakistan, who tells RFI he has heard from people who say they have seen Baradar and other Taliban officials in Karachi.
Baradar, an Afghan, is said to be the Taliban's overall second-in-command below spiritual leader Mullar Muhammad Omar. US officials believe he is in charge of the Taliban's military operations and the Taliban's leadership council.
He would be the highest-ranking Taliban figure to be captured since the US and its allies first went to war in Afghanistan in 2001.
Baradar is currently in Pakistan's custody, with both US and Pakistani agents carrying out interrogations, according to the New York Times.
The paper says it first learned of Baradar's capture on Thursday but delayed reporting it at the request of White House officials, who feared it would interfere with intelligence gathering. The story was published after US officials acknowledged the operation was becoming widely known in Karachi and the surrounding region.
Baradar's reported detention comes in the middle of a major US, Nato and Afghan offensive on a Taliban stronghold in Marjah, Afghanistan, dubbed "Operation Mushtarak". The operation, now in its fourth day, is the largest since the US-led invasion of Afghanistan eight years ago.
The US is spreading the report of Baradar's capture "to make up for the failure in Marjah," claims Yousuf Ahmadi.