Rodriguez told reporters at the Pentagon that the US Army was monitoring camps set up by "Islamic State" (IS), although he added it was not clear just how many were operating.
The general, who heads US Africa Command, told Pentagon reporters that there may be "a couple of hundred" fighters undergoing training at the sites, although details remained sketchy.
"We'll have to just continue to monitor and watch that carefully in the future to see what happens or whether it grows unabated," said Rodriguez. "Right now it's just small and very nascent and we just have to see how it goes."
When asked if the camps might be a target for US airstrikes, Rodriguez said, "That policy discussion is ongoing and we'll see how that goes." He added that that the camps were not being targeted "right now."
The general said it appeared that many of the trainees were members of Libyan militias who were seeking to make a name for themselves and establish connections. He added that it was unclear if they planned to go on to fight for IS in Iraq or Syria.
"It's mainly about people coming for training and logistics support right now, for training sites, and that's what we see right now. As far as a huge command and control network, we have not seen that yet," Rodriguez said.
Parliament forced east
Libya has seen ongoing instability in recent months, with the Islamist group Fajr Libya (Libya Dawn) having seized the capital in Tripoli after a month-long battle with a rival group. The country's internationally recognized Prime Minister Abdullah al-Thinni and his legislature have been forced to work from the east of the country.
Earlier on Wednesday, US Secretary of State John Kerry told a meeting of officials from 60 different countries involved in the coalition against IS that a campaign launched in August which has since involved some 1,000 airstrikes had dealt a "significant" blow to the Sunni group.
Kerry said there was no military coordination with Iran, which has deployed F-4 Phantom jets that it acquired from the US before the 1979 Islamic revolution. However, he said there was an understanding that, in IS, Washington and a mainly Shiite Iran were both fighting a common enemy.
rc/jm (Reuters, AP, AFP)