During the interview, Saif al-Islam Gadhafi said Libya is calm and that the military has not attacked any civilians.
There is a "big big gap between reality and the media reports" Gadhafi told Amanpour. "The whole south is calm. The west is calm. The middle is calm. Even part of the east."
Indeed, there were no reports of violence or clashes on Sunday. However, human rights groups and European officials have put the death toll since unrest began in Libya nearly two weeks ago at hundreds, or perhaps thousands, though it has been virtually impossible to verify the numbers.
Gadhafi loyalists have been out in force, violently trying to keep control over demonstrators seeking government change.
Armed and violent, Gadhafi supporters largely maintain control of Tripoli. On Friday, they reportedly opened fire on a mosque where residents had been holding a sit-in.
Gadhafi loyalists remain in control of Tripoli but he has lost much of the country.
Two prominent U.S. Senators said Washington should recognize and arm a provisional government in rebel-held areas of eastern Libya and impose a no-fly zone over the area - enforced by U.S. warplanes - to stop attacks by the regime. U.S. Secretary of State Hillary Rodham Clinton echoed President Barack Obama's demand for Gadhafi to relinquish power.
"We want him to leave," she told reporters traveling with her Sunday to a U.N. meeting on Libya planned for Monday. "We want him to end his regime and call off the mercenaries and forces loyal to him. How he manages that is up to him."
Asked about Obama's call for his father to step down, he said: "It's not an American business, that's No. 1. Second, do they think this is a solution? Of course not."
As for the U.S. freeze of Libyan assets, he said: "First of all, we don't have money outside. We are a very modest family and everybody knows that."
The Associated Press contributed to this report.