"Tomorrow morning, I'll introduce a resolution that says, 'Why don't we fire the IRS agents that abused their power to target people for their political activities?'" Paul told the network Monday.
“What I find inexcusable is if the president really is outraged by this, someone should lose their job," Paul said.
The Kentucky lawmaker on Tuesday said such a step was an important deterrent to future political targeting.
“I’m not sure who goes, but it surely should be investigated. Anybody who was aware of and approved of targeting people for their political beliefs and speech needs to be fired — never in this position again and made an example of,” Paul said.
Earlier Monday, Sen. Marco Rubio (R-Fla.) said the commissioner of the IRS should resign. Steven T. Miller, the acting commissioner, served as deputy commissioner for services and enforcement when the targeting occurred; Douglas Shulman, the commissioner at the time, saw his term end in November.
The Kentucky lawmaker also hinted again in the Monday interview that he could be interested in replacing President Obama in the Oval Office.
"I guess it's just a coincidence … I don't know why, I keep looking up, and Iowa's on my schedule, New Hampshire's on my schedule, South Carolina," Paul said coyly.
"I want the party to be bigger. I want to be part of the team that grows the GOP," he added.