Months of NATO airstrikes have left his Bab al-Aziziya compound in Tripoli largely demolished.
Scattered battles erupted in Tripoli on Sunday, and it was reported that three of Gadhafi's sons were captured.
However, Saif al-Islam Gadhafi, the one-time heir apparent, showed up at a Tripoli hotel where foreign journalists are based. He arrived in a convoy of armored land cruisers. In a brief interview, he said his father was safe in Tripoli. He claimed the Gadhafi regime is winning and said they were going out to celebrate.
"We broke the back bone of the rebels," Saif al-Islam Gadhafi said.
NATO said it will continue combat air patrols over Libya until Gadhafi and all of his forces surrender.
Gadhafi's whereabouts were unknown, but Pentagon officials say there is no indication that he has left Libya.
The rebels' advance over the weekend met little resistance from troops loyal to the Libyan leader.
The ability of rebels to move into Tripoli in an hours-long blitz showcased the evolution of the opposition fighters who first rose against the regime six months ago, swiftly capturing the eastern part of the vast North African nation but failing to advance westward toward Tripoli even with the help of months of NATO airstrikes.
For months, the rebels - mainly civilian volunteers who took up arms and had little military training - were judged to be big on zeal but short on organization and discipline. However, their stunning success in Tripoli showed a high level of planning, coordination and discipline.
While on vacation in Martha's Vineyard, President Barack Obama released a written statement saying, Tripoli was "slipping from the grasp of a tyrant."
The president also urged the rebels to respect human rights as they look forward to rebuilding the country.
Across the Atlantic, British Prime Minister David Cameron echoed the Obama's statements.
A rebel spokesman who was in Tripoli cautioned that pockets of resistance remained from Gadhafi loyalists. He said that as long as Gadhafi remains at large, the situation was still dangerous.
Since Sunday, a Libyan spokesman said about 1,300 people have been killed and close to 5,000 have been wounded.
The top U.S. official in Libya, Assistant Secretary of State Jeffery Feltman, said whether or not they know where Gadhafi is, he is already part of Libya's past.
"The rebels are clearly taking over the city, taking over the institutions. We just got reports that they've taken over state television," Feltman said. "[Gadhafi] has become for all intents and purposes part of Libya's past and now people need to build Libya's better future."
There have been reports of clashes at Gadhafi's longtime command center Bab al-Aziziya on Monday morning. Government tanks reportedly emerged from the complex and opened fire at rebels trying to get in.
However, there have also been many reports of government troops surrendering to rebel forces without incident.
Local families with ties to Libya are keeping a close eye on what appears to be the impending collapse of Gadhafi's regime.
"We're very, very happy," said Lbyan-American Gaddoor Saidi. "If you lived in Libya, it is a big prison and today you are free again."
One family who left Libya and settled in Southern California several years ago said they've been glued to their TV and the Internet watching the developments in Tripoli. They said watching Gadhafi's regime crumble is a dream come true.
The family has attempted to call relatives in Libya, but they said it has been difficult to get through. They are, however, making contact through social networking sites.
The Associated Press contributed to this report.