SAN FRANCISCO — Senator Rand Paul of Kentucky has been mocked by liberal pundits who accused him of fanning conspiracy theories about a military exercise along the Texas border, an event that some on the far right believe is a covert effort to impose martial law.

But in an interview this weekend, Mr. Paul said he had no idea what the training exercise — known as Jade Helm — was when he was first asked about it last month on an Iowa radio program.

“Someone on a radio program asked me what it was. I didn’t know,” Mr. Paul said after he christened a new work space for his presidential campaign in the Bay Area. He expressed befuddlement at how his comments about “that ridiculous Jade something” had been blown out of proportion.

“I said sure, I’ll ask my staff to look into it because I didn’t know what it was,” he said.

The comments that drew ridicule by people like Bill Maher, who accused Mr. Paul of pandering to the right-wing fringe, occurred on the Jan Mickelson program. Mr. Mickelson brought up the exercise, telling the senator, “I’d like to know what the rest of the story is on that.”

Mr. Paul replied, “We’ll look at that also.”

Other Republicans, like Senator Ted Cruz of Texas, have gone further. Mr. Cruz said he had no reason to doubt the military’s motives, but added that the paranoia was expected because the Obama administration has stoked questions about its honesty. “I understand the reason for concern and uncertainty because the federal government has not demonstrated itself to be trustworthy in this administration.”