Washington (CNN) -- The Pentagon on Monday denied claims that the United States and Iraq have been unable to come to an agreement that would allow some U.S. troops to remain in Iraq after the end of 2011, telling reporters that talks are still going on.
"I'm not sure I would characterize it as an impasse," Defense Department spokesman George Little said. "I think that we continue to work through these issues, and we still have time to go."
The remaining 39,000-plus U.S. troops who remain in Iraq are slated to leave by year's end, and U.S. commanders are "very comfortable" that they can meet that deadline if needed, said Capt. John Kirby, another Pentagon spokesman. U.S. and Iraqi officials have been trying to work out an agreement to leave a U.S. training mission, possibly numbering several thousand, in Iraq past December 31.
At the State Department, spokesman Mark Toner told reporters that he would not discuss details of the talks. But he added, "We're always going to ensure that we have appropriate protections for our people."
"No final decisions have been made. And they're going at, I would say, multiple levels, but certainly bilaterally on the ground in Baghdad," Toner said.
But earlier, a senior U.S. military official with direct knowledge of the discussions told CNN that a key issue regarding legal immunity for U.S. troops who would remain in Iraq after the end of the year had effectively ended the discussion. The Iraqi government's refusal to grant legal protections for any Americans who stay after the current status of forces agreement ends in 2011 has been an issue for the Obama administration, which insists that immunity is necessary.
"Iraqis could not come to meet important terms for the U.S.," according to the senior U.S. official. "I think the discussions on numbers are over."
The United States also could send a limited number of personnel on training missions back into Iraq from Kuwait assuming the immunity issue can be worked out, a senior defense official told CNN on Monday.
A U.S. military official in Iraq, speaking on condition of anonymity, confirmed to CNN on Saturday that the 4th Brigade Combat Team, 1st Armored Division would withdraw early for a number of possible reasons, including the lack of a deal on the legal immunity issue and the fact that the State Department is "standing up" its operations faster than expected.
When family members inquired at a meeting why soldiers from the brigade -- which originally had been expected to be among the last to leave -- were returning months ahead of schedule, they were told by a military official: "Basically, what's happened ... is that the United States and Iraq have not come to an agreement," according to a CNN reporter in attendance.
Additionally, the brigade official told families, "We were over there for a couple of missions. Those missions are finished."
CNN's Chris Lawrence, Chelsea J. Carter and Adam Levine contributed to this report.