Libya's rebels said Tuesday their war against Muammar Gaddafi's regime had entered a “decisive phase” and that victory was possible by the end of the month. That confident claim was echoed by the country's exiled crown prince, and came after Washington said the “days are numbered” for veteran strongman Gaddafi's regime. As the chorus grew, fighting raged across Libya, with the rebels denying they were in talks with a defiant Gaddafi, who predicted a swift victory against both the rebels and NATO. Mansur Saif Al-Nasr, the rebel National Transitional Council's envoy to Paris, said “our forces totally control Zawiyah, which will open the way to Tripoli. This will allow the population there to revolt,” “We are entering a decisive phase. Soon we will liberate all of southern Libya. We hope to celebrate the final victory at the same time as the end of Ramadan” on or around Aug. 31, he told RFI radio. Six Grad missiles hit Zawiyah, sparking a fierce heavy artillery exchange that caused an unknown number of casualties. In a report Tuesday on its operations a day earlier, NATO said it had hit tanks and an armed vehicle near Zawiyah. Gaddafi spokesman Mussa Ibrahim denied the rebel claims, saying regime forces were in “total control” of Zawiyah, and that the insurgent presence was “very weak.” And he said it was actually government troops that had cut the highway leading to Tunisia to “protect people.” Meanwhile, forces loyal to Gaddafi fired a Scud missile for the first time in the country's civil war, a US defense official said, after rebel advances left the Libyan leader isolated in his capital. Rebels fighting to end Gaddafi's 41-year rule seized two strategic towns near Tripoli over the past two days, cutting the city off from its supply lines and leaving the Libyan leader with a dwindling set of options if he is to stay in power. The Scud missile was fired on Sunday morning from a location about 80 km east of Sirte, Gaddafi's home town, and landed east of the coastal oil town of Brega where rebels are fighting for control, the US official said. The missile came down in the desert, injuring no one.