"It is a kind of Taliban establishment which we don't want," Muhammad Ismael Qasemyar, a member of Afghanistan's High Peace Council, told the BBC.
Qasemyar's comments Thursday followed a phone call by U.S. Secretary of State John Kerry to Afghan President Hamid Karzai to try to defuse the situation. He told Karzai the Taliban's office in Qatar was removing the flag and the nameplate designating the building as the "Islamic Emirate of Afghanistan" would be replaced by one saying "Bureau of Peace Talks."
Qatar's Foreign Ministry said the office opened in Doha "is the political office of the Taliban in Afghanistan, and is not the political office of the Islamic Emirate of Afghanistan," Khaama Press reported.
On Wednesday Karzai said peace talks in Qatar were suspended until "foreign powers" allowed the process to be run by Afghans. He also suspended security talks with the United States on the U.S. presence in Afghanistan after the NATO mission ends in 2014.
Qasemyar told the BBC negotiators objected to a statement made by a Taliban official when the office was established, which indicated the militants would have relations with entities such as the United Nations.
"Unless our demands are accepted, we are not going to take part in Qatar talks," he said.
The first formal meeting between U.S. and Taliban representatives had been expected to occur soon, but now it is unclear what role Afghan officials will play, the BBC said.
Karzai opposes bilateral peace discussions between the Taliban and the United States and has long called on the Taliban to participate in a peace process led by Afghanistan.