Hundreds of troops loyal to Libya's interim government are closing in on one of ousted leader Muammar Gaddafi's few remaining strongholds.
Fighters have moved on Bani Walid from three sides, warning Gaddafi loyalists to surrender or be attacked.
The desert town hit the headlines last month as rumours spread that two of Col Gaddafi's sons had travelled through it as they fled south from Tripoli.
Some reports say Gaddafi family members may still be in the town.
On Saturday, the head of Libya's interim governing NTC said its soldiers were also laying siege to Col Gaddafi's birthplace in Sirte, as well as Jufra and Sabha.
National Transitional Council Chairman Mustafa Abdel Jalil said the towns were being given humanitarian aid, but had one week to surrender "to avoid further bloodshed".
Tripoli move delayed
One commander told the BBC that anti-Gaddafi forces were closing in on Bani Walid from the north, east and west on Sunday morning.
"We are now on the border of Bani Walid, between Tarhouna and Bani Walid," Moftah Mohammed told the BBC. "We are coordinating with the rebels from Misrata. God willing, we are hoping to enter the town today or tomorrow."
Another fighter, Abdulrazzak Naduri, had earlier said that Bani Walid had until just 08:00 on Sunday to surrender or face military action.
Early reports suggested that Saif al-Islam and Mutassim Gaddafi had holed up in the desert town surrounded by armed supporters, and were ready to make a final stand there, says the BBC's Kevin Connolly in Tripoli.
But the situation is less clear-cut than it first appeared, he adds, with hard-core Gaddafi forces having fled Bani Walid while other loyalist elements were ready to negotiate.
It is likely there are moves afoot to set up talks to avoid a showdown, says our correspondent.
Either way, analysts say it is important for the new national army to consolidate its control of all of the country to allow it to form a meaningful new government and to remove the threat from the old regime. Taking Bani Walid is key to that.
Col Gaddafi's whereabouts remain unconfirmed; his spokesman Moussa Ibrahim told Reuters in a telephone interview that the ousted leader was somewhere in Libya, safely surrounded by loyal supporters.
Meanwhile, the NTC is stepping up its efforts at reconstruction, setting up a supreme security council to protect Tripoli.
But it has said its leadership will not now move from Benghazi to Tripoli until next week, with Mr Jalil the last to go.
This could mean a delay in the opposition formally assuming the role of the new government and raise fears of a power vacuum in the capital, correspondents say.
Ian Martin, a special adviser to the UN secretary general, arrived in Libya's capital on Saturday to try to boost international efforts in the country's redevelopment.
