Meetings between Afghan leadership and Taliban figures are ongoing, but the two sides are nowhere near a peace deal and in fact are not even to the point of negotiating one, Special Representative Richard Holbrooke said Sunday.

"I think the press has left the impression that negotiations of the type which ultimately ended the war in Vietnam in 1973 and ultimately ended the war in Bosnia in 1995 are somehow breaking out. That is just not the case," he said on CNN's GPS with Fareed Zakaria show Sunday morning.

"What we've got here is an increasing number of Taliban at high levels saying, hey, we want to talk," Holbrooke explained. "I think this is a result, in large part, of the growing pressure they're under from General Petraeus and the ISAF command."

Holbrooke was adamant that -- whatever talks are taking place between the government of President Hamid Karzai and leaders of some of the insurgent groups -- it should not be called a "negotiation."

"I would not use that word," he said. "I know what a negotiation looks like... Let's not leave the viewers with the impression that some kind of secret negotiation like the famous secret negotiations on Vietnam, is taking place, because it's not."

Holbrooke warned that a peace agreement of the sort seen in past conflicts is unlikely because there is no titular head of the insurgency with whom to strike a deal.

"There's no Ho Chi Minh. There's no Slobodan Milosevic. There's no Palestinian Authority. There is a widely dispersed group of people that we roughly call the enemy," he said. "So the idea of peace talks, to use your phrase, or negotiations, to use another phrase, doesn't really add up to the way this thing is going to evolve."

Holbrooke said he had no personal information that the Pakistani military or intelligence services have been trying to thwart rapprochement between the Afghan government and the Taliban, as the New York Times has reported. He refused to publicly call for the Pakistani military to increase its effort against terrorist groups in North Waziristan, saying that Pakistan knew the Obama administration's position on the issue.

"I'm not here to defend the Pakistani military or to attack them," he said.

Overall, Holbrooke's take on the progress of the war effort was cautious, if not entirely bleak.

"It's certainly not another Vietnam, for reasons you and I discussed before. And it is certainly not hopeless. But anyone who doesn't recognize what a daunting task it is, is misleading," he said. "And the American public should understand that this is not going to be solved overnight. It is going to be a difficult struggle."

Holbrooke was not asked about the stunning admission by Karzai that his office received bags full of cash from Iran. Holbrooke did attend a meeting last week in Rome with dozens of Special Representatives from various countries dealing with the Afghan war where the Iranian government was also represented.