Local and foreign media reported earlier that his father had fled the country to Brazil or Venezuela and his son had taken over as head of the country. But this was not confirmed by any Libyan official sources.
"We will fight to the last minute, until the last bullet," he said.
Seif al-Islam said Libya's parliament would convene on Monday to discuss a clear reform agenda, while the government would also raise wages.
"We will have to lay down a constitution for the country," he said, pledging to make reforms in future.
Gaddafi's son said if the situation got out of control, every Libyan has to carry arms to defend himself, because the country would have bloodshed.