Libyan leader Muammar Gaddafi's son denied Sunday that his family had secreted billions of dollars out of the country, as he scornfully dismissed a UN vote calling for freezing their assets.

"First of all, we don't have money outside," Saif Al-Islam Gaddafi told ABC television's "This Week" programme.

"We are a very modest family and everybody knows that. And we are laughing when they say you have money in Europe or Switzerland or something. Come on, it's a joke."

His comments came a day after the UN Security Council slapped a travel ban and assets freeze on Gaddafi and his inner circle.

The 15-member council unanimously adopted a resolution that also imposes an arms embargo on Libya, where the United Nations says more than 1,000 people have been killed, and condemns violence incited "from the highest level" of the Libyan leadership.

But the younger Gaddafi insisted that his country was calm -- despite daily riots, shootings and protests -- and denied reports that the military had shot and killed hundreds of Libyans and possibly many more.

He pointed to a "big big gap between reality and the media reports."

"The whole south is calm. The west is calm. The middle is calm. Even part of the east," the younger Gaddafi said.

He also reiterated his father's defiant vow not to give up power.

"Listen: nobody is leaving this country. We live here, we die here," he insisted. "This is our country. The Libyans are our people. And for myself, I believe I am doing the right thing."

The second oldest of the longtime leader's children nevertheless conceded that the regime is in "a difficult situation."

Asked to respond to a call by US President Barack Obama that his father step down, Gaddafi answered: "It's not an American business, that's number one.

"Second, do they think this is a solution? Of course not."

He denied the government had used military force against Libyan protesters, and dismissed claims that support for the regime was eroding across the country.

"We didn't use force," added Gaddfi, who received a doctorate degree from the London School of Economics. "We still have people around us."

He balked at reports the regime had used live fire, including by military aircraft, against Libyan civilians.

"Show me a single attack, show me a single bomb," he told ABC.

"The Libyan Air Force destroyed just the ammunition sites," Gaddafi said. "That's it."

Asked about Libyan diplomats who have resigned their post, he said they were misinformed.

"You know, we are the victims of miscommunication," he said. "They were under the influence of a strong media campaign, well-organised. So, you know, they are human beings at the end."