Kabul, Afghanistan (CNN) -- Political figures from Pakistan and Afghanistan are sitting down this week in Kabul for a dialogue aimed at ending the 9-year-old Afghan war, in what one Afghan official called a "new phase" in building bridges and making peace with the Taliban.
Former Pakistani government officials and political party leaders met Afghan leaders at the Serena Hotel on Tuesday and Wednesday, Farouq Wardak, Afghanistan's education minister, told CNN in an exclusive interview.
Wardak said the Taliban did not participate, though Mullah Zaeef -- the ex-Taliban ambassador to Pakistan who served time in the detention center at Guantanamo Bay, Cuba, and is now living openly in Kabul -- did attend.
Two other sources confirmed Zaeef's presence at the meetings.
Wardak said that "there have been approaches by various groups claiming to be the Taliban" to the Afghan government who've expressed interest in joining mainstream Afghan society, and he called the effort a "new phase" in what has been a long process.
"They want to join the main social political stream of the Afghan society. And they want to live in peace," he said.
Wardak said there are challenges in engaging diplomatically with the Taliban. In the 1990s, there was a Taliban hierarchy and "a kind of structure."
"And the structure was so that if you can talk to the people on the top, the message can go down easily. But today that does not exist. This is to the negative side of it," he said.
"This is a process. A process may have different steps. At some steps we may be talking with individual and lower rank of Taliban. But it may go to that we reach the middle level of Taliban, even upper level of Taliban," Wardak said.
An aide to Wardak said the United Arab Emirates ambassador and the U.N. Special Representative to Afghanistan, Staffan de Mistura, were also present at the latest meetings.
The talks are part of the so-called Abu Dhabi process, started by the EastWest Insitute, and they follow a meeting held in June in Abu Dhabi.
Five sources, who asked not to be named because of the delicacy of the discussions, confirmed the meetings.
The talks "are entirely of a consultative nature," said one of the sources, noting that the purpose of the dialogue is "to build trust between sections of Afghan society and Pakistan."
While one Afghan political figure stressed that the effort was not initiated by the Afghan government, the group met with President Hamid Karzai for lunch Wednesday to report on the progress of the meeting.
The Washington Post reported Wednesday that Taliban representatives and the Karzai government "have begun secret, high-level talks over a negotiated end to the war," citing Afghan and Arab sources. But is unclear whether the Abu Dhabi process dialogue in Kabul is the same process cited in that report.
The Pentagon made it clear Wednesday that Karzai is operating independently in his efforts to reach out to the Taliban.
"We've consistently said that reconciliation is an Afghan program, Afghan-led," Pentagon spokesman Col. David Lapan said in an off-camera question-and-answer session with journalists. "So it is really up to them. I don't know that we have any veto power or any decision making in that."
Lapan said Afghan leaders would inform the United States., including the commander of U.S. forces, Gen. David Petraeus, if military operations were an obstacle.
"It would be up to the Karzai government to let Gen. Petreaus know if our actions and efforts were somehow interfering with reconciliation efforts," Lapan said.
Caitlin Hayden, spokeswoman at the U.S. Embassy in Kabul, said the United States has not been not involved in reported talks and isn't in a position to comment on them.
"Our position on reconciliation is one that we have stated consistently: The United States supports an Afghan-led process of reconciliation and reintegration that seeks to bring back into society those who cease violence, break ties with al Qaeda and its affiliates, and live under the Afghan Constitution, including provisions that protect the rights of all Afghan men and women," she said.
Candace Rondeaux, senior analyst with the International Crisis Group, a widely respected nongovernmental, nonprofit organization, said she believes the discussions are basically "talks about talks" and warned that it's too soon to begin predicting peace.
The Washington Post report cites sources saying that "for the first time they believe that Taliban representatives are fully authorized to speak for the Quetta Shura, the Afghan Taliban organization based in Pakistan, and its leader, Mohammad Omar.
Rondeaux cautioned that "nobody knows what the Quetta Shura really wants" and "how many members of the midlevel command are on board.
"There has been a noticeable and quite pronounced split between members of the Quetta Shura and the command structure out in the field."
There have been contacts between the Afghan government and Taliban members in recent years, such as meetings in Saudi Arabia, and the government has focused on reconciliation efforts wtih the Taliban.
The Karzai government recently announced the creation of a High Peace Council that was assigned the mandate of paving the way toward peace with the Taliban, which was thrown out of power in Afghanistan when the United States invaded the country in 2001.
Petraeus told journalists last month that "there are very high-level Taliban leaders who have sought to reach out to the highest levels of the Afghan government."
Petraeus expressed support for Afghan government efforts to negotiate with the Taliban, saying "this is the way you end insurgencies."
But the Afghan government tried to downplay his remarks.
"There are no substantive negotiations or substantive dialogue with the armed opposition," said a Karzai spokesman.
The Taliban rejected Petraeus' claims and ridiculed the creation of a peace council.
The EastWest Institute said in a report published after the opening meeting in June that "there is no military solution to the conflict in Afghanistan" and explained that a "dialogue leading to political settlement should therefore begin soon."
It also said the Afghan-Pakistani relationship is "key to any successful political settlement."
CNN's Ivan Watson and Charley Keyes contributed to this report.