He said that the government would "fight to the last bullet" to stay in office.
In a TV address to the nation broadcast as anti-government protests spread to the capital Tripoli, he admitted that the military had over-reacted against protesters.
But he accused opposition groups and Islamists of trying to break up Libya.
He played down casualties, suggesting that at most 14 people, not 200, died in clashes in the eastern city of Benghazi.
And he promised "reform and democracy", saying that Libya's legislative forum would meet on Monday.
Heavy gunfire could be heard across Tripoli on Sunday evening, and witnesses spoke of tear gas and live ammunition being used against protesters by the security forcesColonel Gaddafi is the Arab world's longest-serving leader, having ruled the oil-rich state since a coup in 1969.
The Middle East region is seeing a wave of pro-democracy protest, fuelled by the fall of Egypt's Hosni Mubarak on 11 February, and long-time Tunisian President Zine al-Abidine Ben Ali in JanuaryDrunkards and thugs'
Urging Libyans to "stop the bloodshed and stand as one for Libya", Sayf Gaddafi said they had a "real chance of reform and democracy".
He praised his father, saying he was not like Mr Mubarak and had received thousands of calls from people willing to come to Libya and defend him.
"Some people" had been killed, he conceded, but foreign media were exaggerating the violence and reports of high death tolls were "imaginary", he said.
Troops had opened fire on protesters because they were not trained to handle civil unrest, he argued.
He accused "opposition elements" living abroad of trying to initiate an Egypt-style Facebook revolution in Libya.
"They have started a campaign to bring Libya to a point reached by Egypt and Tunisia," he said.
"Security forces have pre-empted this and arrested some of the people involved. A few people have died and violence against the police has escalated... This is what happened in Benghazi."
He warned of the threat of civil war, saying "everyone" in the country was armed and, if war started, Libyans would be "mourning hundreds and thousands of casualties".
He confirmed that protesters had seized control of some military bases and tanks in eastern Libya, and said "drunkards and thugs" were driving tanks about the streets.
He also said that "African mercenaries" were being used against the government - a charge protesters have made against the government itself.
'Grave concern'In comment released before Sunday night's speech by Sayf Gaddafi, the US state department said it was "gravely concerned with disturbing reports and images coming out of Libya".
UK Foreign Secretary William Hague told the Libyan leader's son in a phone call of London's "grave concern" at the escalation of violence.
Verifying information from Libya has been difficult amid a government clampdown on the internet and media communications. Libyan authorities have imposed severe media restrictions.
But by Sunday evening, reports suggested that anti-government forces in Benghazi had largely won control of the city after days of brutal suppression by government forces.
Unconfirmed reports said a military garrison there had either fallen to the opposition, or switched sides.
In Tripoli, people could be heard chanting slogans calling for the toppling of the regime on Sunday.
Credible reports suggested that a police station had been burnt down and a building belonging to the country's ruling party had also been attacked and set ablaze.
In the Gourghi area of the city, witnesses said tear gas and live ammunition were used against anti-government protesters. Tear gas was said to have filled the entire neighbourhood, with those sitting outside their homes forced to to go inside.
The area around Tripoli's largest university was said to be dominated by anti-government protesters calling for the fall of the regime
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