KABUL, Afghanistan — Afghan President Hamid Karzai on Friday accused the United States of stonewalling the investigation into the killings of 16 Afghan civilians and suggested more than one soldier may have been involved.

The claims again escalated tensions between Afghanistan and the United States at a time of flagging public support for the war in both nations and uncertainties over how to end it.

While Karzai routinely has lashed out at his chief military ally over the issue of civilian casualties, the Afghan president described himself this time as at "the end of the rope."

After a somber palace meeting with relatives of victims of Sunday's massacre, Karzai seemed to support villagers' insistence that the soldier held by the U.S. military, identified by Pentagon officials Friday as Army Staff Sgt. Robert Bales, of Lake Tapps, did not act alone.

"They believe it's not possible for one person to do that," Karzai said, citing one man's account of the killing spree that spanned two villages in Kandahar province. "In his family, in four rooms, people were killed, women and children were killed, and they were all brought together in one room and then put on fire. That, one man cannot do."

The president also said he was not satisfied with how U.S. officials were conducting the investigation.

The Afghan army chief "has just reported that the Afghan investigation team did not receive the cooperation that they expected from the United States," Karzai said. "Therefore, these are all questions that we'll be raising, and raising very loudly, and raising very clearly."

The U.S. Embassy in Kabul declined to comment, and a spokesman for NATO's International Security Assistance Force said the military would not address Karzai's assertions. "We don't have anything to add or to comment on regarding his statements," Lt. Col. Jimmie Cummings said.

Televised footage from the gathering of relatives in the palace reflected the frustration and rage among the victims' families, to the point of rejecting offered compensation for their losses.

"Mr. President, I do not want money," said a villager sitting next to Karzai. "I want the killer to be punished, punished, punished."

On Thursday, Karzai demanded NATO troops pull out of villages and stay instead on major bases, a move that would undermine the Iraq- and Vietnam-style strategy the United States has been using to gradually put the Afghan army in charge of the war in areas where the Taliban are strongest.

Tension also persists over the contentious issue of night raids on civilian locations in search of Taliban leaders, as well as questions about how long foreign troops should remain in Afghanistan and under what conditions.

While Karzai is known to be wary of an expeditious withdrawal of U.S. troops — experts say the government is not strong enough to prevent an almost-certain civil war — he has to play to Afghans' sentiment against the decadelong U.S. presence.

More than 3,000 civilians were killed last year in wartime violence, according to the United Nations, but the world body blamed more than three-quarters of the deaths on insurgents.

On Friday, Karzai seemed to absorb a measure of the relatives' anger over the killings of nine children, three women and four men early Sunday in the Panjwai district. "This has been going on for too long," he said. "This is by all means the end of the rope here. ... This behavior cannot be tolerated. It is past, past, past the time."

Karzai's angry demeanor and combative remarks stood in contrast to what White House officials described as a calm conversation between him and President Obama earlier Friday, in which U.S. officials said the two leaders broadly agreed on a range of issues.

According to a White House statement, the purpose of the call, made just after midnight EDT, was for Obama "to offer his best wishes and congratulations to President Karzai and his wife on the birth of their daughter." The statement amounted to a reiteration of Obama's schedule for ending the war and an indication Karzai agreed with it.

The Afghan president's version of the call said the leaders "affirmed that they share the goal of building capable Afghan security forces ... with the lead for combat operations shifting to Afghan forces, with U.S. forces in support, in 2013."

White House spokesman Jay Carney said Karzai's call for an early NATO withdrawal "was clearly a subject of the conversation." But despite the apparent disparity in tone and substance of the accounts, Carney said "the two men were very much on the same page."

In another development Friday, Turkish forces suffered their worst losses of the war when 12 soldiers died in a helicopter crash on the outskirts of Kabul. Four Afghan civilians on the ground also were killed. NATO and Turkish officials said there was no evidence of enemy fire.

Turkey, one of only two majority-Muslim countries in NATO, has about 1,800 troops in Afghanistan and leads NATO operations in Kabul province. It is exempted from combat operations.

Washington Post reporter Karen DeYoung and correspondent Ernesto Londono contributed to this report. Information from the Los Angeles Times also is included.