Afghan President Hamid Karzai on Friday accused the United States of stonewalling an investigation into the killings of 16 Afghan civilians and suggested that more than one soldier may have been involved in the massacre.

Karzai’s claims escalated again the tensions between Kabul and Washington at a time of flagging support for the war from the U.S. and Afghan publics — and uncertainties over how to end it.

Although Karzai has often lashed out at his chief military ally over civilian casualties, the Afghan president described himself this time as at “the end of the rope.”

After a somber palace meeting with relatives of the victims of Sunday’s massacre, Karzai seemed to support the villagers’ insistence that the Army staff sergeant being held by the U.S. military did not act alone.

“They believe it’s not possible for one person to do that,” Karzai told reporters, citing one man’s account of the killing spree, which 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 probe into the rampage.

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 here 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 continued sense of frustration and rage among the victims’ families.

“Mr. President, I do not want money,” said a villager sitting next to Karzai, rejecting offered compensation. “I want the killer to be punished, punished, punished.”

On Thursday, Karzai demanded that 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 following to gradually put the Afghan National Army in charge of the war in areas where the Taliban is 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.

Although 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 — but faces Afghan sentiment against the decade-long U.S. presence.

On Friday, he seemed to absorb a measure of the relatives’ anger over the killings of nine children, three women and four men 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.”

He added: “This behavior cannot be tolerated. It is past, past, past the time.”

Karzai’s angry demeanor and combative remarks stood in contrast to identical statements issued by his office and the White House that described a calm conversation between him and President Obama earlier Friday morning.

According to the statements, the purpose of the call, made just after midnight Washington time, was for Obama “to offer his best wishes and congratulations to President Karzai and his wife on the birth of their daughter.” Together, they amounted to a reiteration of Obama’s schedule for ending the war and an indication that Karzai agreed with it.

The statements 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 that Karzai’s call for an early withdrawal of coalition troops “was clearly a subject of the conversation,” but he added that “the two men were very much on the same page.”

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

Gen. John R. Allen, commander of the International Security Assistance Force, said in a statement, “My deepest sympathies go out to the families of these ISAF service members and the Afghan civilians who died as a result of this unfortunate incident.”

Turkey, one of 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.

Staff writer Karen DeYoung in Washington and correspondent Ernesto Londoño in Kabul contributed to this report.