Kabul, Afghanistan ? The American campaign in Afghanistan suffered a double blow Thursday: The Taliban broke off talks with the U.S., and President Hamid Karzai said NATO should pull out of rural areas and speed up the transfer of security responsibilities to Afghan forces nationwide in the wake of the killing of 16 civilians.

The moves represent new setbacks to America’s strategy for ending the 10-year-old war at a time when support for the conflict is plummeting.

Part of the U.S. exit strategy is to transfer authority gradually to Afghan forces. Another tack is to pull the Taliban into political discussions with the Afghan government, though it’s unclear that there has been any progress since January.

Although Karzai has previously said that he wanted international troops to transition out of rural areas, the apparent call for an immediate exit is new. Karzai also said he now wants Afghan forces take the lead for countrywide security in 2013, in what appeared to be a move to push the U.S. toward an earlier drawdown.

A statement released by Karzai’s office said that during his meeting with visiting U.S. Defense Secretary Leon Panetta, the president “requested that the international forces come out of Afghan villages and stay in their bases.”

Karzai also said that the “Afghan security forces have the ability to provide security in the villages of our country,” the statement said.

But a senior U.S. official said Karzai did not make any demands to have U.S. troops leave villages immediately. The official, who spoke on condition of anonymity to disclose details of a private meeting, said it’s unclear that the U.S. would be able to pull all of its troops out of the villages even by 2013. He noted that the U.S. plans to continue counterterrorism operations and advising the Afghan forces around the country.

A rapid pullout from rural areas would have a devastating effect on U.S. ability to challenge the Taliban on the battlefield.

Unlike the Iraq war, where most combat was in towns and cities, the Afghan conflict is a struggle to secure rural hamlets and remote mountain valleys used by the militants to move in and out of sanctuaries in neighboring Pakistan.

It would essentially mean the end of the strategy of trying to win hearts and minds by working with and protecting the local populations.

Karzai spoke as Afghan lawmakers were expressing outrage that the U.S. flew the soldier suspected of gunning down 16 civilians early Sunday in two Afghan villages to Kuwait on Wednesday night. They were demanding that the suspect, a U.S. Army staff sergeant, be tried in the country.