As few as 3,000 American soldiers could remain in Iraq after the withdrawal of the tens of thousands of security forces now stationed there, several American news media have learned.

Although a final agreement on the drawdown of America’s military presence has yet to be reached with Iraq, the White House could come close to meeting the president’s promise to disengage the United States from the country altogether.

Some 46,000 American troops are currently in place in Iraq. Under the 2008 Status of Forces Agreement signed by the Iraqi government and the Bush Administration, all forces were scheduled to depart by December of this year but a minimal security presence is likely to stay behind.

Defense secretary Leon Panetta told reporters on Tuesday that “no decision has been made with regard to numbers of troops” although the Iraqi authorities had “indicated a desire for trainers to be there” after the December deadline expires, he said.

American and Iraqi military officials agree that Baghdad needs foreign assistance in defense of its air space, borders and territorial waters. The country barely has an air force yet while its navy consists entirely of small coastal patrol and support vessels. The army has an ambivalent, if not hostile relationship with Kurdish soldiers in the north where separatists could pose a security threat in the future, especially if the civil unrest in Syria, which is also home to a sizable Kurdish minority, continues to linger.

Several top American lawmakers were dismayed by the news. Democrat Dianne Feinstein, who chairs the Senate intelligence committee, worried that the reduction in force levels came “too fast.” Republicans John McCain and Lindsey Graham, both national-security hawks, stated that they were “deeply troubled” by the news and wondered whether a 3,000-strong troop presence might not “lack the capabilities and authorities necessary to help Iraqis ensure stability across the disputed territories in northern Iraq.”

The New York Times reported that the American commander in Iraq, General Lloyd Austin, had called for a force of 14- to 18,000 soldiers to stay in the country.