NSA interceptors purportedly shared some intercepts of highly personal conversations, including "phone sex."
Fort Gordon spokesmen referred all questions Thursday to the NSA.
NSA spokesman Patrick Bomgardner told The Associated Press that some of the allegations have already been investigated by the agency and found to be unsubstantiated.
"Others are in the investigation process," he said.
A comment from the White House wasn't immediately available.
If the allegations are true, they could reignite a political fire storm over the Bush administration's post-Sept. 11 eavesdropping operations and its efforts to collect vast quantities of data about Americans' tax, medical and travel records; credit card purchases; e-mails; and other information.
President Bush and other senior officials have repeatedly asserted that after the Sept. 11 attacks, the NSA monitored only the private communications of Americans who were suspected of links to terrorist groups without court orders.
The recently adopted eavesdropping law requires the government to get court permission to listen in on American communications. The previous version required only the attorney general's approval.
"At NSA, the law was followed assiduously," said Mark Mansfield, a spokesman for CIA Director Mike Hayden, who headed the NSA during the period in question.
The allegations follow the release Tuesday of a study by a government advisory group that questions how useful the intercepts and another technique known as data mining are at ferreting out terrorist plots.
"The information sought by analysts must be filtered out of the huge quantity of data available (the needle in the haystack problem)," says a two-year, 352-page study by the National Research Council for the Department of Homeland Security.
"Even under the pressure of threats as serious as terrorism, the privacy rights and civil liberties that are the cherished core values of our nation must not be destroyed," the report warns.
An ABC News report Thursday quoted two former military linguists at Fort Gordon saying that the country's largest intelligence agency routinely recorded calls to homes and offices by hundreds of Americans in the Middle East between 2001 and 2007. The interviews were scheduled to be aired Thursday evening on ABC's Evening News and Nightline .
The ABC News story quoted former Navy Arabic linguist David Murfee Faulk, 39, as saying that he and other intercept operators at the Fort Gordon NSA facility monitored calls by Americans in Baghdad's Green Zone.
"Calling home to the United States, talking to their spouses, sometimes their girlfriends, sometimes one phone call following another," said Mr. Faulk, who served at the Army post from late 2003 until November 2007.
A second former Fort Gordon intercept operator, Adrienne Kinne, 31, an Army Reserve Arabic linguist, told ABC News that conversations monitored by NSA operators included calls by journalists and aid workers.
"These were just really everyday, average, ordinary Americans who happened to be in the Middle East, in our area of intercept and happened to be making these phone calls on satellite phones," Ms. Kinne said, describing the calls as "personal, private things with Americans who are not in any way, shape or form associated with anything to do with terrorism."
Ms. Kinne, who worked at Fort Gordon for two years beginning in November 2001, contended that "collecting" the calls of innocent Americans hobbled the NSA's ability to find genuine terrorism-related material.
"By casting the net so wide ... it's harder to find that piece of information that might actually be useful to somebody," she said, echoing the National Research Council's findings. "You're actually hurting our ability to effectively protect our national security."