FBI Director Robert Mueller

Washington (CNN) -- FBI Director Robert Mueller said Thursday he is concerned about the potential for terrorists mounting cyber attacks and that the bureau is working "to stay ahead of these threats, both at home and abroad."

"While to date terrorists have not used the Internet to launch a full-scale cyber attack, we cannot underestimate their intent," Mueller testified to a Senate Appropriations subcommittee in which lawmakers pressed him about what additional funding and laws may be necessary to combat the cyber threat.

Mueller did not provide many details during the public session, but later met with senators behind closed doors to provide additional information.

Mueller noted that terror groups are becoming more "cyber savvy." As examples, he cited al Qaeda in the Arabian Peninsula, which publishes an online magazine called Inspire, and the Somali group Al-Shabaab, which has its own Twitter account.

More importantly, however, he said, terrorists are "using cyberspace to conduct operations."

Republican Sen. Lindsey Graham of South Carolina asked Mueller whether a cyber attack suspect tied to al Qaeda would be treated differently than a regular criminal suspect. Many members of Congress have said terror suspects are better handled by the military than going through a criminal court process.

But Mueller did not debate the issue, saying when a cyber intrusion happens, his agency's goal is to find out who is behind the computer.

"At the point in time of an intrusion, you don't know whether it's going to be a country, a terrorist or the 18-year-old kid down the block," he said.