Fighting has flared in two key areas of the Libyan capital, Tripoli, for a third day as rebel fighters battle forces loyal to Col Muammar Gaddafi. Gunfire and explosions have been heard near a hotel held by government troops, as well as the area around the Libyan leader's Bab al-Aziziya compound. Overnight, Col Gaddafi's son Saif al-Islam appeared in public, days after rebels claimed he had been captured. He insisted the government had "broken the backbone" of the rebel offensive. Saif al-Islam arrived at the Rixos Hotel, where foreign journalists are based, in a government vehicle in the early hours of Tuesday morning. Saif al-Islam told the BBC: "We have broken the backbone of the rebels." He added that by moving into Tripoli, the rebels had fallen into a trap. "We gave them a hard time, so we're winning," he said. The BBC's Matthew Price, who spoke to him, said he seemed confident and full of adrenalin. Battle for control Our correspondent says there have been sustained bursts of gunfire, mortars and rocket-propelled grenades (RPGs) around the hotel on Tuesday, but that it is impossible to ascertain if it is coming from pro-Gaddafi forces or is the result of the rebels pushing back. Both sides say they control most of the capital. The BBC's Rupert Wingfield-Hayes, who is with a rebel column on the western outskirts of Tripoli, says commanders have decided to concentrate all their forces on the heavily fortified Bab al-Aziziya compound. They believe the key to ending this conflict is to capture or kill Col Gaddafi, our correspondent says. Nato told the rebels to pull back so they could bomb Bab al-Aziziya on Tuesday morning, he adds. It is not clear whether Saif al-Islam escaped from custody, or if he had never been captured in the first place. On Sunday, the rebels said they had captured him, along with other members of the Gaddafi family. The International Criminal Court (ICC) - which has issued arrest warrants for Saif al-Islam, Col Gaddafi and his intelligence chief, Abdullah al-Sanussi, on charges of crimes against humanity - said on Monday it was negotiating with the rebels to transfer Saif al-Islam to its custody at The Hague. But on Tuesday, it denied having received confirmation from the rebels that Saif al-Islam had been detained. An ICC spokesman said different rebel factions had given different information. Saif al-Islam said he did not care about the ICC arrest warrant. Asked if Col Gaddafi was safe and in Tripoli, he replied: "Of course." The Libyan leader has not been seen in public for months, although he broadcast an audio message on Sunday night, urging residents to "save Tripoli" from the rebels. Next moves Meanwhile, members of the rebel National Transitional Council (NTC) in Benghazi say they plan to fly to the capital on Wednesday to start work on forming a new government. NTC chairman Mustafa Abdul Jalil has said all Gaddafi aides will face justice and fair criminal trials. "I will stand trial for years I served as a minister in the Gaddafi government," he told a news conference in Benghazi. He advised Libyans to be tolerant, saying they should "avoid taking matters into their own hands and... abide by court rulings". The NTC leadership has expressed concern about revenge attacks by some of the mosaic of different groups which make up the revolutionary army. In other developments: * Turkey has announced it is giving $300m (£181m) to the NTC, including funds to form the new government * Nato says it has destroyed two rocket launchers that were aiming fire at the town of Brega * Col Gaddafi's eldest son, Muhammad, reportedly escaped from rebel custody hours after being detained * The International Organization for Migration (IOM) said a boat it sent to Tripoli to evacuate migrant workers was unable to dock because of the security situation * Egypt and Bahrain formally recognised the NTC as the legitimate government of the Libyan people The rebels swept into Tripoli at the weekend, but after a swift advance, they met stiff resistance in a number of areas on Monday. World leaders have urged Col Gaddafi to step down. US President Barack Obama said elements of the Gaddafi regime continued to pose a threat. The uprising against Col Gaddafi's 41-year rule began in February. The rebels held the east of the country and pockets of the west, before making their push towards the capital at the weekend. Nato air strikes have been targeting Col Gaddafi's troops, acting on a UN mandate to protect civilians.