Tripoli, Libya Six months after a ragtag group of poorly trained rebels set out to topple the Libyan regime, the fighters appeared Monday to be on the brink of ending Moammar Gadhafi's 42-year rule.

On Monday, rebel forces were engaged in a barrage of clashes with Gadhafi forces on the leader's home turf, Tripoli.

"A great majority of the capital of Tripoli is under freedom fighters' control," said Guma El-Gamaty, the Britain-based coordinator for the rebels' Transitional National Council.

Rebels on Monday afternoon pulled back from an area near Green Square -- which rebels are renaming Martyrs' Square -- to coordinate some sort of offensive in the city, although it was not immediately clear what they were planning.

Gadhafi's regime remained in control of at least three sites in the city -- a hospital, a military barracks and the Rixos hotel, where international journalists are staying, El-Gamaty said.

Gadhafi's forces in Tajoura, where the hospital is located, were negotiating their surrender Monday morning, said Jumma Ibrahim, a rebel military spokesman.

Rebel fighters clashed with Gadhafi forces near the Rixos Hotel, one of the remaining Gadhafi strongholds in Tripoli, said CNN's Matthew Chance, who is at the hotel.

In Zawiya -- a key coastal city that appeared to be under rebel control -- residents celebrated by firing guns in the air, setting off fireworks and chanting, "Libya is free!" And in Benghazi, one resident called the rebel gains as joyous as "New Year's Day."

But Gadhafi's whereabouts remains uncertain, El-Gamaty said Monday.

He said the opposition believes Gadhafi is either hiding in Tripoli or has fled to southern Libya or to nearby Chad or Algeria.

"Those are the only two neighboring countries that have been showing support for him," El-Gamaty said.

Rebel units have been deployed to a northern coastal highway -- a main thoroughfare?to Tunisia "to get rid of one of the last Gadhafi forces positioned in the northern coastal stretch," said Jamal Kor, a rebel field commander.

Kor said rebels hope the entire coastal stretch between Ras Ajdir, Tunisia, and Tripoli "will be in rebel hands" by Monday afternoon.

"We have tried to persuade Gadhafi forces to surrender, but to no avail, " Kor said.

Confident that victory was close, the rebel government began making plans to govern.

El-Gamaty told CNN Monday that it will take 18 to 20 months to create a political framework for a new Libyan government.

Though fighting in Tripoli continues, "Libya is under the control of the TNC," said Ali Suleiman Aujali, the rebel government's ambassador to the United States. Aujali added that Gadhafi brigades have raised the white flag in the key town of al-Brega.

CNN could not independently confirm his claim.

Sporadic gunfire and explosions coming from the direction of Gadhafi's Bab al-Aziziya compound could be heard Monday morning.

Much of Bab al-Aziziya has already been destroyed by NATO airstrikes, and a fight for the compound might be more symbolic in nature.

NATO, operating under a U.N. Security Council resolution authorizing the use of force to protect Libyan civilians, has conducted more than 7,500 strike sorties in Libya since NATO began the military operation in March.

Libyans seeking Gadhafi's ouster rejoiced Sunday after news that two of the ruler's sons -- Saif al-Islam and Saadi -- had been arrested by opposition forces.

On Monday, a third Gadhafi son, Mohammed, was also taken into custody.

A man identified as Mohammed Gadhafi told Al Jazeera during a live telephone interview early Monday that rebels had entered his home.

"I'm being attacked right now. This is gunfire inside my house. They are inside my house," he told Al Jazeera.

As for the other four sons, El-Gamaty said, "we think they are either hiding or they have run away."

The fate of Saif al-Islam Gadhafi -- an outspoken defender of his father's regime -- could lie in the hands of the International Criminal Court.

Chief Prosecutor Luis Moreno-Ocampo said the court plans to begin negotiating Monday for his transfer to the Netherlands. Saif al-Islam is wanted for crimes against humanity, along with his father and the elder Gadhafi's intelligence chief, Abdullah al-Sanussi.

But Aujali, the rebel government ambassador, said he thinks the Libyan people should decide what to do with the sons.

There was no immediate reaction from Libyan government officials to the arrests.

On Sunday, Gadhafi took to the airwaves several times urging citizens, including women, to fight the rebels -- whom he called "very small groups of people who are collaborators with the imperialists."

"Get out and lead, lead, lead the people to paradise," he said.

Libyan government spokesman Musa Ibrahim told reporters late Sunday night that about 1,300 people had been killed and about 5,000 wounded in fighting in the previous 12 hours.

"(The city) is being turned into a hellfire," he said from Tripoli.

"Every drop of Libyan blood shed by these rebels is the responsibility of the western world, especially NATO's countries."

NATO Secretary-General Anders Fogh Rasmussen said the Gadhafi regime is "clearly crumbling."

"The sooner Gadhafi realizes that he cannot win the battle against his own people, the better -- so that the Libyan people can be spared further bloodshed and suffering," Rasmussen said in a statement Monday.

If the Gadhafi regime falls, it would follow revolutions in Tunisia and Egypt this year in what is known as the Arab Spring. A spate of other countries in the region -- including Bahrain, Yemen and Syria -- have also seen protests by citizens demanding more freedom and a change in regime. In many cases, these demonstrations have been met with brute force.

U.S. President Barack Obama said Sunday night the momentum against Gadhafi's regime has reached a tipping point."Tripoli is slipping from the grasp of a tyrant," Obama said. "The surest way for the bloodshed to end is simple: Moammar Gadhafi and his regime need to recognize that their rule has come to an end."CNN's Sara Sidner,Jomana Karadsheh, Kareem Khadder, Raja Razek, Matthew Chance, Christine Theodorou, Kamal Ghattas, Roba Alhenawi, Holly Yan, Chelsea Carter and Barbara Starr and journalist Mike Mount contributed to this report.

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