Two British papers are reporting that the United Kingdom and the United States have agreed on a date for troop pullout of Iraq, but the Pentagon's top general said Sunday that is untrue.

Joint Chiefs of Staff Chairman Peter Pace said conditions on the ground will determine when U.S. and coalition forces will depart Iraq.

"We're going to do exactly what we said we were going to do, which is to make the assessments of situations on the ground. The commanders in the theater will make their recommendations up the chain of command, and that will eventually get through the secretary of defense, to the president, for decisions about U.S. troop levels," Pace told "FOX News Sunday."

The British reports, citing an unnamed senior British defense source, say the plan is to bring U.S. and British troops home within the year. Britain's Sunday Telegraph reports the alleged strategy is the result of acceptance in London and Washington that coalition troops are "the main obstacle to peace" in Iraq.

Pace also rejected reports that Iraq is spiraling toward civil war. Iraq's elected officials continue to bicker over forming a new government, which has delayed Parliament from meeting since before the Dec. 15 election installing a permanent government.

Even with sectarian violence on an upsurge and pressure mounting on Prime Minister Ibrahim al-Jaafari to give up his bid for a new term, Pace said he does not believe that the country is imploding.

"Right now, the Iraqi army has over 100 battalions that are in the field. The Iraqi police have over 30 battalions that are in the field. There's plenty of Iraqi security forces to do the work that needs to be done to maintain peace between Iraqis," he told "FOX News Sunday."

Ending the insurgency depends not only on military efforts but also on whether the Iraqi government can give the people what they want, he said.

"The fact that it's taking a while for that government to form — you have many, many different groups that need to be represented in a fair and representative government. They're working hard at it. Democracy is not clean, not easy, but they're working real hard, and that government, when it does form, will have the support of a much improved and improving military," he said.

"I do not believe it has deep roots," Pace said of the insurgency. "I do not believe that they're on the verge of civil war."

Pace acknowledged on another Sunday talk show that "anything can happen," but said he believed the restraint showed by Iraqis after a recent bombing of a sacred mosque showed that Iraqis aren't interested in more bloodshed.

Despite increasing worry among Americans that the three-year-old campaign is going badly, Pace said that much progress is being made toward training Iraqi forces to take over security of the country — something officials hope will eventually allow U.S. troops to leave

Asked how things are going, Pace said: "I'd say they're going well. I wouldn't put a great big smiley face on it, but I would say they're going very, very well."

While operations are more peaceful in Afghanistan, the U.S. military is commencing a criminal investigation into the death of Army Corporal Pat Tillman, the National Football League player turned-Army ranger who was killed in Afghanistan.

Tillman gave up his multi-million dollar contract with the Arizona Cardinals to fight for the United States after the Sept. 11, 2001, terror attacks. He was killed in April 2004. Tillman's family was first told he died by enemy fire, then came the admission it was by friendly fire — the alleged result of "gross negligence" by U.S. soldiers in his unit.

The criminal probe is the fifth investigation into Tillman's death. Pace said it's being done in order to provide as much information as possible to Tillman's family members, who have been unsatisfied with prior investigations, saying they suspect a cover-up.

"I think every step of the way that the folks who have been responsible for investigating it have been trying to do the right thing, but, as we should be doing, we review the investigations. They go up the chain of command. Folks look at them to make sure they have complete information. If there's not complete information, they send it back," Pace said.

"In this case, it's unfortunate that it has to be looked at again, but I'm satisfied that it is being looked at again, because if one of the reviewing officials decided that there was something that had to be looked at, we should do that," he added.

Seven soldiers have already been reprimanded for their role in Tillman's death, but no high-ranking officials have been disciplined. One lawmaker from Tillman's hometown in California is pushing for a congressional investigation, saying he worries about the Army investigating itself.

FOX News' Megyn Kendall and The Associated Press contributed to this report.