Kabul, Afghanistan (CNN) -- The U.S. soldier accused in the killing of 16 Afghan civilians was identified Friday by sources, even as Afghan President Hamid Karzai expressed doubt over U.S. authorities' account of events that led to the rampage.
A military source and a senior defense official identified the suspect as Staff Sgt. Robert Bales. He has not been officially named by the military, which says its policy is to wait until a soldier is charged.
Earlier Thursday, Karzai suggested in a meeting at the presidential palace in Kabul with relatives of the dead that the Americans had not been frank about what happened and had not helped his effort to find out.
"We tried to talk to the soldier involved, but there was no cooperation from America," Karzai said. He expressed skepticism that only one person was involved in the shootings. "Based on what you are saying, the killer was not just one person," he told the villagers.
The soldier is accused of leaving a remote combat outpost on foot early Sunday and heading to neighboring villages in the Panjwai district of Afghanistan's Kandahar province.
In the village, he allegedly went house to house on a killing rampage.
Asked whether he had seen surveillance footage apparently shot at the soldier's base, Karzai questioned the authenticity of the video.
"The army chief and the police chief have been shown, or I believe their representatives have been shown, a video of the surveillance that they have, which has not been satisfactory to our team," he said. "Not convincing."
Karzai said that he had spoken to U.S. President Barack Obama earlier Friday and that Obama had been upset by Afghanistan's response to the attack.
Karzai suggested that the relationship between the two countries was at a breaking point.
"It is by all means the end of the rope here," he said. "The end of the rope that nobody can afford such luxuries anymore."
Four Afghan homes had been affected by the shooting, Karzai said.
A village elder, who did not identify himself but said he had lost a family member in the shooting, told the president, "Now (the Americans) are offering us money. I don't want money. I want justice."
Karzai said, "We have not asked for compensation. The Afghan government will not ask for compensation. We ask for justice, not compensation."
The White House said in a statement that Obama and Karzai had agreed to discuss further Karzai's call for the withdrawal of foreign troops from Afghan villages and longstanding concerns regarding night raids and house searches.
Obama also congratulated Karzai and his wife on the recent birth of a daughter.
White House spokesman Jay Carney said that the two leaders were "very much on the same page" in their discussions and that Obama had acknowledged the recent challenging times for Karzai.
Karzai received a report from an Afghan investigative team before talking Thursday with U.S. Defense Secretary Leon Panetta in Afghanistan.
The report's findings were "clearly on his mind" during his session with Panetta, a senior U.S. defense official said. The official spoke on condition of anonymity because of the sensitivity of the issue.
It was not immediately known whether Karzai planned to release the findings to the families or the public.
Afghans have been demanding that the soldier, who was flown out of Afghanistan by the U.S. military, be returned to stand trial.
His attorney, John Henry Browne, said the soldier, who was originally taken to Kuwait, was expected to arrive Friday at a U.S. military prison at Fort Leavenworth, Kansas.
Karzai called the shootings a cruel act against the people of Afghanistan and told Panetta that Afghans have lost trust in the international force, the presidential palace said in a statement.
Karzai also recommended that American troops withdraw from villages, the statement said.
Speaking about the meeting, Defense Department spokesman George Little said that "the issue of the villages noted in the press release did arise, but it was in the context of a shared commitment" to an agreed-upon plan that outlines the time frame for handing over security duties to Afghan forces by 2014.
The plan, known as the Lisbon Strategy, was adopted during a summit in Lisbon, Portugal, in November 2010.
In the Panjwai villages, the soldier shot and killed nine children, three women and four men, witnesses and Afghan authorities said. The U.S. military has not confirmed the number of casualties.
Afghan lawmaker Muhammad Naim Lalai accused the United States of showing "a fake video" intended to convince people that the soldier acted alone.
Lalai said he was one of several Afghan officials shown a surveillance video from the soldier's base in Kandahar province.
"We were shown a video in which a soldier climbs the wall of a military base and then goes indoors and pulls his bulletproof jacket off and then puts his arms up to surrender himself," Lalai said.
The United States has not confirmed it showed the video to Afghans, though a U.S. official has said footage taken by an "aerial asset" shows the soldier lying on the ground outside the base and then attempting to "low crawl" back into the outpost.
The soldier, who is based at Joint Base Lewis-McChord near Tacoma, Washington, belongs to the 3rd Stryker Brigade Combat Team, 2nd Infantry Division, according to a congressional source who was not authorized to speak publicly.
He was on his first tour to Afghanistan but had deployed to Iraq three times.
CNN's Larry Shaughnessy, Chris Lawrence, Carol Cratty, Barbara Starr, Casey Wian and Ninette Sosa and journalist Ruhullah Khapalwak contributed to this report.