Rebels in the Libyan city of Misrata say they have pushed government troops back from its outskirts.
Misrata, the only city in western Libya under rebel control, has been under siege from forces loyal to Col Muammar Gaddafi for two months.
The UN aid chief called for a pause in hostilities to ease Libya's humanitarian crisis, and described the situation in Misrata as dire.
In Tripoli, blasts were heard overnight in what reportedly were Nato strikes.
Eyewitnesses spoke of at least five air strikes which are believed to have targeted Col Gaddafi's compound and other government buildings.
The Libyan government has so far made no public comments about the explosions.
The rebels say Misrata remains surrounded, but that they have advanced about 30km (18 miles) to the west.
An AFP correspondent in Misrata said the rebels were now in control of a stretch of coastline heading towards the capital.
A rebel spokesman, Mohammed, told the BBC: "We've pushed Gaddafi away from Misrata."
He said the morale of the rebels was high, and that "they want to keep going".
Reda, another rebel, told Reuters news agency there had been fighting in the east, west and south of the city as well as near the airport.
"The revolutionaries control the western side while the (pro-Gaddafi) brigades are still holding the south-eastern side of the airport," he said, adding that they had been aided by recent Nato air strikes.
Libyan state media has said Nato aircraft bombed "military and civilian targets" in Misrata and the nearby town of Zlitan on Monday.
Reporting restrictions mean the claims from both sides cannot be independently verified.
Medical sources say at least 300 people have been killed by the weeks of fighting in Misrata.
On Monday, Valerie Amos, the UN's under-secretary for humanitarian affairs, said: "In Misrata, which is at the forefront of our concerns, shelling and fighting has been ongoing in parts of the city for over two months. Stocks are available, but some people are running short of food, water and other basics."
A Red Cross ship successfully docked in Misrata on Monday, bringing medical equipment, baby food and spare parts for electrical and water systems.
The port has become a lifeline for the city, allowing refugees to leave and supplies to be brought in, but has come under repeated attack from pro-Gaddafi forces.
The BBC's Andrew Harding in Benghazi says the rebels have managed to get arms into Zlitan and are hoping its residents will rise up.
But the town is still controlled by pro-Gaddafi troops, he adds, so it will not be easy for the rebels to achieve that goal.
Nato Secretary General Anders Fogh Rasmussen has told CNN that Col Gaddafi has been "stopped in his track" and that his time is running out.
"The game is over for Gaddafi. He should realise sooner rather than later that there's no future for him or his regime," he said.
Meanwhile, the UNHCR says hundreds of people are feared to have drowned when a boat broke up shortly after leaving Tripoli port.
The agency has called on all ships using the Mediterranean to be prepared to offer assistance to the often unseaworthy vessels carrying migrants from Libya to Europe.