Taliban spokesman Zabiullah Mujahid said the liaison office will conduct negotiations with the international community. He did not say when it would open.
For the United States and its allies, the idea of a Taliban political office in the Qatari capital Doha has become the central element in efforts to draw the insurgents into peace talks.
"Right now, having a strong presence in Afghanistan, we still want to have a political office for negotiations," said Mujahid. "In this regard, we have started preliminary talks and we have reached a preliminary understanding with relevant sides, including the government of Qatar, to have a political office for negotiations with the international community."
Mujahid's emailed statement also said the Islamic Emirate of Afghanistan -- the name of Afghanistan under Taliban rule -- , has "requested for the exchange of prisoners from Guantanamo."
He was referring to a Taliban demand that the U.S. military release about five Afghan prisoners believed to be affiliated with the Taliban from the prison at Guantanamo Bay, Cuba.
The Taliban are holding Bowe Bergdahl, a 25-year-old U.S. Army sergeant from Hailey, Idaho, who is the only U.S. soldier held by the insurgents. He was taken prisoner June 30, 2009, in Afghanistan.
A senior U.S. official told The Associated Press last week that Washington plans to continue a series of secret meetings with Taliban representatives in Europe and the Persian Gulf region next year.
The U.S. outreach this year has progressed to the point that there was active discussion on two steps that the Taliban seek as precursors to negotiations, said the official, speaking on condition of anonymity due to the sensitivity of the issue.
Trust-building measures under discussion involve setting up a Taliban headquarters office and the release of the Afghan prisoners from Guantanamo.
Last Tuesday, President Hamid Karzai said his government would accept the Taliban establishing a liaison office in Turkey, Qatar or Saudi Arabia for the purpose of holding peace talks.