WASHINGTON — President Barack Obama called Afghan President Hamid Karzai in the wee hours Friday, seeking clarity on the Afghan leader’s demand that U.S. forces pull out of Afghan villages, a key tenet of the current military strategy.

Karzai claimed he stood firm on that demand, which took U.S. leaders by surprise a day earlier.

“He asked, ‘Did you announce this?'” Karzai told reporters in Kabul. “I said, ‘Yes, I announced it.'”

The White House said the two leaders agreed to continue discussing the matter.

“I think that the two men were very much on the same page,” about the overall plan to gradually hand over responsibility for fighting to Afghan forces and remove foreign forces by the end of 2014, White House press secretary Jay Carney said.

Karzai lashed out at the United States on Friday, saying he is at the “end of the rope” following a massacre of Afghan villagers allegedly carried out by an American soldier stationed in a rural outpost. The soldier’s lawyer provided new details of his background, including three tours in Iraq, and claimed the soldier felt double-crossed by the military when sent to Afghanistan last year. The 38-year-old suspect’s name has not been released.

The Obama administration is seeking to put the best face on an Afghanistan policy called into question by the announcement from the U.S.-backed Karzai government, and by word from the Taliban insurgent movement that it was shelving talks with the Americans.

A senior U.S. official familiar with the discussions said U.S. officials presume the timing of the Taliban announcement following Sunday’s killings is an attempt to gain greater leverage over the United States.

The unusual early-morning phone call from Obama is a strong indication the administration is concerned, although the White House said the first purpose of the call was to congratulate Karzai on the birth of a baby daughter.

Karzai had demanded Thursday that U.S. troops leave rural Afghan areas and stay on bases until they finish a withdrawal of troops by the end of 2014. The war effort has been set back in recent days by the 16 deaths, and earlier by the inadvertent burning of Qurans by U.S. troops.

Although Karzai previously has said he wanted international troops to transition out of rural areas, the apparent call for an immediate exit is new.

Amid confusion among U.S. military officials and diplomats about just what Karzai was asking, U.S. officials tried to minimize the differences.

Pentagon press secretary George Little said Thursday the issue reflects Karzai’s “strong interest in moving toward a fully independent and sovereign Afghanistan as soon as possible.”

“We share President Karzai’s interest,” Little said. “We believe it needs to be done in a responsible manner.”

The soldier accused of the shootings was part of far-flung “village stability” operations favored by former war commander Gen. David Petraeus and seen as a central element of the counterinsurgency strategy to build trust and skills among local Afghan forces and neighborhood militias.

Although the U.S. has walked away from basic pillars of the counterinsurgency strategy, the policy to keep soldiers working and living alongside rural populations has continued.

It was never popular with Karzai, who has said the insurgent problem in his country springs from support across the border in Pakistan, not from unrest in villages. Critics of the U.S. and NATO military plan long have said that a large military footprint, especially in conservative rural districts, encourages violence and bolsters the Taliban argument that they are fighting a foreign occupier.

U.S. spokesmen said the administration will press on with trying to reconcile Afghanistan’s government and Taliban forces willing to renounce terrorism, despite Thursday’s announcement by the militants that they were suspending contacts with the United States. The last substantive talks between U.S. officials and Taliban representatives was in January, and two initiatives to build trust and move toward real peace talks are in limbo.

In a statement in English on its website, the Taliban said U.S. negotiators had “turned their backs on their promises and started initiating baseless propaganda.” The Taliban also accused the U.S. of making new demands in the talks, a charge Carney denied.

The announcements from Afghanistan on Thursday struck at both elements of the twin-track U.S. exit strategy, which calls for a gradual transfer of security authority to Afghan forces and U.S. talks with Taliban insurgents as a seed for larger political reconciliation talks with the Afghan government.

The Obama administration has endorsed negotiation with the insurgents as the best hope for reaching a political settlement in Afghanistan. Direct talks begun in secret last year have foundered before, and several people familiar with the contacts characterized the latest news as a temporary but expected setback. They spoke on condition of anonymity to describe sensitive diplomacy.

In claiming that the U.S. had failed to deliver of past promises, the Taliban were referring to a plan the U.S. has backed publicly to open a Taliban political office in the Gulf state of Qatar, as the Taliban had requested. That plan, although reluctantly endorsed by Karzai, apparently has been delayed by an internal Taliban debate about a public renunciation of international terrorism and U.S. objection to the Taliban plan to brand the office the representative of the “Islamic Emirate” of Afghanistan.

The U.S. has made that renunciation a condition for opening the office, and considers that title illegitimate.

The Taliban also seek release of five prisoners held at the U.S. military prison in Guantanamo Bay, Cuba. The AP previously has reported that the U.S. agreed in principle to transfer the prisoners to custody in Qatar, and U.S. officials have publicly acknowledged the idea is in play. The Taliban statement said the U.S. side has “initially agreed upon taking practical steps regarding the exchange of prisoners,” but complained that the Americans are now “wasting time.”

The Taliban have maintained they want to negotiate only with the United States, the largest donor and largest military force in Afghanistan, instead of the Karzai government. The Associated Press previously reported that the U.S. side had agreed to greater Afghan government participation in future talks. That shift appears to underlie the Taliban claim of a change in terms, although their statement was not specific.