Mr. Karzai, please shut up.
Whenever somebody admits to a secret, we need to ask a few questions:
1. Why is this person telling the public about this secret?
2. Are they doing it for a reason?
3. Are they just plain incompetent, or simply loose-lipped?
4. What advantages are to be gained from admitting to the secret?
In this case, I'm not too sure, because in the long term the Afghan's have everything to gain from negotiating with the Taliban. Coming to some kind of an agreement can stop the fighting, bring some measure of stability to Afghanistan, and quite possibly increase Karzai's expected lifespan. In the short term (and this is how decisions tend to be made), however, a continuation of the war means money continues to be pumped into Afghanistan and Karzai's corrupt government remains in place. In this sense, it is not in Karzai's interest to stop the fighting because an end to fighting probably means a new government structure and a new government means no more Karzai on top.
Therefore, if it is in Karzai's interest to prolong the fighting, admitting that his government is secretly negotiating with the Taliban completely kills the chances of a possible settlement-- easily! He single-handedly demonstrated his untrustworthiness to any negotiating party (the U.S. included) and simultaneously pulled the rug out from underneath the Taliban. Job well done!
No serious and competent negotiating partner would admit to secret negotiations, and a trustworthy partner would recognize that if the negotiations are being kept a secret, there's probably a reason for it. In the Taliban's case, secret talks are necessary because that has been their stance all along, namely, not negotiating. Understandably, if they are going to talk, those talks would be held in secret (at least at first). Karzai killed that chance and betrayed their scintilla of trust.
I don't like to think that Karzai is purposefully sabotaging a possible reconciliation, but I also don't think that he is an idiot and would let such a secret casually slip in front of a reporter. It is for that reason that I have to assume that he did it on purpose, and that his only purpose was to kill the chances of reconciliation.
Not surprisingly, the Taliban have rejected they have been conducting negotiations, and the chances of that happening in the future seem even more distant.
The only other possibility I can imagine is that the Taliban are fractured, and that one group is indeed interested in negotiating while another group is against it (hence the conflicting signals). Either way, the process is dead for the foreseeable future thanks to Karzai's comments.