Libya conflict: Defiant Saif al-Islam Gaddafi reappears
He turned up in a government vehicle at a hotel held by loyalists, a day after the rebels said they had detained him.
A BBC correspondent said Saif al-Islam seemed confident and full of adrenalin.
On Monday the rebels met strong resistance from pro-Gaddafi forces as they continued their push. Both sides say they control most of Tripoli.
Saif al-Islam Gaddafi turned up at Hotel Rixos in the early hours of Tuesday.
He told the BBC's Matthew Price: "We have broken the backbone of the rebels." He added that by moving into Tripoli, the rebels had fallen into "a trap".
"We gave them a hard time, so we're winning," he said.
Saif al-Islam Gaddafi, 39, had been widely regarded as a likely successor to his father. On Sunday the rebels claimed they had captured him, along with other members of his family.
Saif al-Islam also said he did not care about an arrest warrant issued by the International Criminal Court in The Hague on charges of crimes against humanity.
Asked if Col Gaddafi was safe and in Tripoli, he replied: "Of course."
He also went to his father's Bab al-Azizia compound and told three journalists accompanying him: "Tripoli is under our control. Everyone should rest assured."
The Libyan leader's whereabouts are still unclear. A diplomatic source told AFP news agency that Col Gaddafi could still be at the compound. He has not been seen in public for months, although he has broadcast audio messages from undisclosed locations.
In a broadcast late on Sunday, he urged residents to "save Tripoli" from the rebels.
Members of the rebels' National Transitional Council in Benghazi say they plan to fly to the capital on Wednesday to start work on forming a new government.
A BBC correspondent in Benghazi says there is optimism in their ranks that by the middle of the week Tripoli airport will be secure enough to allow them to move.