Tripoli, Libya (CNN) -- 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. "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. But Gadhafi's regime remained in control of at least three parts of the city -- a hospital, a military barracks and 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. 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 throughoughfare 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 Ghaddafi 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. Celebrations in Tripoli's Green Square -- renamed Martyrs' Square by the rebels -- dampened after rebels told CNN that they'd heard Gadhafi army forces were heading their way. 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 7,400 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. The next day, a third Gadhafi son 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. "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. 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."