Anti-government fighters say they made advances on several towns in the eastern part of the country.
Forces loyal to Moammar Gadhafi rallied in Tripoli to show they are in control of the capital city.
They used helicopter gunships, rockets and gunfire to push back the rebels.
ABC News reported that a U.N. humanitarian assessment team will be allowed to enter Tripoli.
Earlier, Libyan warplanes opened fire on rebel forces moving toward the city of Sirte, a stronghold of Gadhafi.
Ultimately, those rebels have their sights set on the capital city of Tripoli. Over the weekend, rebel forces also took over two strategic oil locations - Brega and Ras Lanouf.
Fierce ground battles were raging around the front line between the two towns about 30 miles apart, Ras Lanouf and Bin Jawad to the west.
Witnesses reported heavy air attacks by helicopters on the rebel forces as well as heavy fighting on the ground. A small military base, three hangars and a small building in Ras Lanouf were also destroyed by a warplane.
In Tripoli, the city of 2 million that is most firmly in Gadhafi's grip, residents awoke before dawn to the crackle of unusually heavy and sustained gunfire that lasted for at least two hours.
Some of the gunfire was heard around the sprawling Bab al-Aziziya military camp where Gadhafi lives, giving rise to speculation that there may have been some sort of internal fighting within the forces defending the Libyan leader inside his fortress-like barracks. Gadhafi's whereabouts were unknown.
Gadhafi supporters attacked the rebel-held city of Misrata, which is 120 miles east of Tripoli. The downtown area was shelled with mortars and tank artillery.
Misrata residents said the shelling began Sunday morning and that the rebels were fighting back with rocket propelled grenades and anti-aircraft guns.
Saturday, rebels near Ras Lanouf said they shot down a Libyan Air Force plane that crashed in the desert. The headless bodies of the pilots were found at the scene. There is no evidence as to exactly how that plane came down.
The Libyan uprising that began on Feb. 15, inspired by rebellions in neighboring Tunisia and Egypt, has been sliding toward a civil war that could be prolonged, with rebels backed by mutinous army units try to topple Gadhafi's 41-year-old regime.
At the same time, pro-Gadhafi forces have tried to conduct counteroffensives to retake the oil port of Brega and in the rebel-held city of Zawiya west of Tripoli - where bloody street battles were reported over the weekend.
The U.S. has moved military forces closer to Libya's shores to put military muscle behind its demand for Gadhafi to step down immediately. But Washington has expressed wariness about talk of imposing a "no fly" zone over the North African nation to prevent the Libyan leader from using his warplanes to attack the population.
At the same time, the U.N. has imposed sanctions, and Libya's oil production has been seriously crippled by the unrest. The turmoil has caused oil prices to spike on international markets.
Hundreds, perhaps thousands, have died in the violence with tight restrictions on media making it near impossible to get an accurate tally.
The Associated Press contributed to this story.
