Former Sen. Joe Lieberman (I-Conn.) told a House committee this morning that the Obama administration’s rush to blame the Benghazi attack on an anti-Muhammad video underscored the White House’s narrow definition of Islamic terrorism.

“It was obviously a terrorist attack by any generally held definition of terrorism,” Lieberman said at the House Homeland Security Committee, which was examining the administration’s “false narrative” that al-Qaeda is on the run.

“They obviously weren’t just there to have a good time,” he said of the terrorists gathered outside the U.S. diplomatic facility, and “even if it was somehow affected by the video, still it was terrorism.”

“Why there was hesitancy to do that?” Lieberman said of the administration’s lack of immediate recognition that a terrorist attack took place on the anniversary of 9/11.

He singled out as a big part of the problem the administration’s insistence on defining the enemy as just those inspired by al-Qaeda or a loosely linked affiliate.

“When you limit the category,” the senator said, and refuse to acknowledge the enemy is “violent Islamic extremists … you miss part of the enemy.”

Lieberman noted that this insistence on classification means the administration lacks intelligence on Islamic terrorists not affiliated with al-Qaeda.

The State Department just this month designated three branches of Ansar al-Sharia as foreign terrorist organizations, he noted, highlighting this lack of understanding.

“Sometimes the world doesn’t cooperate with a presidential narrative, and I think that’s where we are,” Lieberman said.