Update (11:53 a.m. EST): The Taliban says it hasn't met with Afghan officials and doesn't plan to, CNN is now reporting, citing an email from the militant group:

"The Islamic Emirate strongly rejects Karzai's remarks and adds that the Islamic Emirate has never met with the representatives of the powerless Kabul administration, and has made no decision to hold talks with the Karzai government, even in the future," the Taliban said in a statement e-mailed to CNN.

The United States hasn't commented on Karzai's claim, The New York Times reported, after reaching out to the National Security Council for comment: "Tommy Vietor, a spokesman for the United States National Security Council, declined to comment on Mr. Karzai’s statement, but has made clear in the past that there are many steps that would have to be taken before substantive peace negotiations could begin."

Original: The U.S. and Afghanistan governments have been in quiet contact with the Taliban, holding three-way meetings as the Taliban gets tired of carrying on its fight, Afghan President Hamid Karzai told The Wall Street Journal. But Afghanistan's ambassador to Pakistan says that the three-way contact was only "exploratory" and couldn't yet be called peace talks. The hard-line group leading a years-long insurgency in Afghanistan is ready to figure out a way to end its fight, Karzai told the Journal in an exclusive Wednesday interview: "People in Afghanistan want peace, including the Taliban. They're also people like we all are. They have families, they have relatives, they have children, they are suffering a tough time. I'm inclined to say that yes, they do want peace."

But Umar Duadzai, the ambassador to Pakistan, said in a follow-up chat with Reuters Thursday that consequential talks were still a ways off: "When there's talks, it's supposed to be between the Afghan government and the Taliban. We have not reached to that stage although we wish to reach to that stage." So the Taliban is meeting with the Afghan and U.S. governments in order to talk about how to start meeting with the Afghan government in order to talk peace. Got it.