The opening of the Taliban office was heralded as the best chance of bringing to a peaceful end 12 years of bloody war despite its rocky beginnings.
But the peace process ran aground almost immediately when Kabul objected to the wording of its name, saying it was tantamount to the establishment of a rival government office, not a political office.
"There is an internal discussion right now and much anger about it but we have not yet decided what action to take," Shaheen Suhail, the Taliban's spokesman in Qatar told The Associated Press in a telephone interview. "But I think it weakens the process from the very beginning."
Afghan President Hamid Karzai reacted furiously on Tuesday to the sign, temporarily withdrawing from talks and put a quick end to negotiations with the United States over a security accord that is to lay out protection for US forces that will remain in Afghanistan after the withdrawal of NATO combat troops at the end of 2014.
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But Suhail said the incident has frustrated and angered some within the militant movement who said the Taliban have been meeting with representatives of dozens of countries and holding secret one-on-one meetings with members of Karzai's High Peace Council on several occasions, always under the banner of the Islamic Emirate of Afghanistan.
"Now the process is being weakened at the beginning and not being given a chance," he said. "This is very bad for the Afghan people, for the international community."
Suhail said the Taliban had not been notified of talks with Dobbins today but he hoped for cooler heads to prevail.
"Everyone should save the process. Give a chance to the process. In one day everything cannot be resolved," he said.
"This is a very secondary thing and not important. I am also surprised that it should derail the process."
The Taliban have already agreed to hand over US Sgt Bowe Bergdahl, captured by the Taliban in 2009, in exchange for five Taliban held in the US prison at Guantanamo Bay, Cuba.
Suhail also addressed issues of a cease-fire and women's rights saying they can "all be part of the agenda and discussed.