The site of the camp is in the same Libyan city as the U.S. Consulate that was overrun by Libyan gunmen on Sept. 11. The attack ended with the deaths of U.S. Ambassador Chris Stevens and three other Americans.
U.S. officials are looking to build a roughly 400-man counterterrorism force consisting of Libyan nationals between 19 and 25 years old, Obeidi said.
It remains unclear whether the official in charge of training the Libyan paramilitary force was a member of the U.S. military or the intelligence community.
"The American team asked us for a tour of our base and we granted them permission to walk around freely," said the militia commander.
"They stood with many of our men taking down information. They asked them about their ages, backgrounds, their tribal loyalties. They wanted to know what kind of training they had received, if any," he added.
Training could be held in Libya or the recruits could be taken overseas to learn their trade, according to the Libya Shield chief.
Libya's Shield is a patchwork force formed from factions of various rebel groups who helped oust former Libyan strongman Moammar Gadhafi from power last March.
The group mainly consists of fighters who, after Gadhafi's death, refused to join the new government, claiming the ruling members are mostly Ghadhafi loyalists, according to the report.
The U.S. training effort comes nearly a month after White House counterterrorism chief John Brennan met with top Libyan military and intelligence officials in Tripoli to discuss the Benghazi strike and what could be done to prevent another attack from happening.
In recent months, many senior Republican lawmakers have hammered the White House for the lack of security at the Benghazi outpost at the time of the September attack.
The administration's initial claims the attack was the result of an anti-American protest gone violently wrong also drew a firestorm of criticism from Republicans, including allegations of a White House cover-up of the attack.
GOP presidential hopeful Mitt Romney has spent much of his campaign attempting to leverage the incident as proof of President Obama's foreign policy failures.
But last Thursday, U.S. intelligence officials unveiled a highly detailed account of the raid, including information disclosing that officers at the CIA annex in Benghazi went to the consulate to attempt a rescue after they were unable to receive help from local militias.
Further, intelligence officials said there was no delay or order to “stand down,” and no interference or second-guessing from officials in Washington.
Recent reports also claim the diplomatic mission of the U.S. Consulate in Benghazi was a cover for a large-scale CIA intelligence operation inside Libya run out of the State Department facility.
The spartan outpost in Benghazi was one of several intelligence hubs set up by CIA in the aftermath of the Libyan revolution that ended with Gadhafi's death.
American intelligence and special operations forces are on the ground in Libya, collecting information on groups and individuals suspected of participating in the Sept. 11 assault.
The Pentagon's elite Joint Special Operations Command, in conjunction with the CIA and other U.S. intelligence agencies, is assembling "target packages" on suspected militants associated with the attack, should the president give the order for the strikes.
The range of counterstrike operations being considered by DOD and the intelligence community run the gamut from armed drone strikes to covert kill or capture raids, according to recent news reports.