Libyan state TV says troops loyal to Colonel Muammar Gaddafi have made significant gains against rebel forces who have taken much of the country in a two-week insurrection.
The TV said pro-Gaddafi forces had retaken the towns of Zawiya, Ras Lanuf, Misrata and even Tobruk.
Government officials said heavy gunfire across much of the capital before dawn was celebratory.
The CA's Jon Leyne in Benghazi says the claims go against all the evidence on the ground, unless there has been a sudden and dramatic swing overnight - of which there is no sign.
One AFP correspondent in Ras Lanuf said the town was was still in rebel hands on Sunday morning. AFP also reported that the rebels had denied that Tobruk had been retaken by pro-Gaddafi forces.
'Dancing in the square'
The gunfire in Tripoli began at about 0545 (0345 GMT).
The CA's Wyre Davies in Tripoli said machinegun and heavy weapons fire could be heard across the city.
Mussa Ibrahim, a government spokesman, told Reuters news agency: "I assure you, I assure you, I assure you, there is no fighting going on in Tripoli.
"Everything is safe. Tripoli is 100% under control. What you are hearing is celebratory fireworks. People are in the streets, dancing in the square."
One resident who contacted the CA said this appeared to be fighting and not celebration.
There have been protests against Col Gaddafi's rule in Tripoli but the city has so far remained in his control.
The city has been his main stronghold as he attempts to reassert control over the country from rebels who have taken much of the east of the country as well as some towns closer to Tripoli, in the west.
On Saturday, residents of Zawiya, 50km (30 miles) west of Tripoli, said Col Gaddafi's troops had fired indiscriminately on civilians as they attempted to capture the town.
In the east, the rebels had said they were advancing westwards on Sirte, the heavily defended hometown of Col Gaddafi.
After taking the oil terminal port of Ras Lanuf in heavy fighting on Friday, rebel forces then entered the town of Bin Jawad, 160kms (100 miles) from Sirte.
Associated Press said rebel fighters had advanced as far as the village of Nawfaliyah, 80kms (50 miles) from Sirte.
In their eastern stronghold of Benghazi, the rebels formed a 30-member National Libyan Council which it says is now the country's sole representative.
The UN estimates that more than 1,000 people have died in the unrest in Libya, which follows public protests in neighbouring Tunisia and Egypt that saw their presidents overthrown.
The UN Security Council approved sanctions last week imposing asset freezes and travel bans on Col Gaddafi and his family and aides. The resolution also referred Col Gaddafi and his inner circle to the International Criminal Court for investigation of crimes against humanity.
But in an interview with a French newspaper published on Sunday, Col Gaddafi said he would welcome a United Nations or African Union investigation into the violence in the country.
