Libya's new leaders gave Gadhafi loyalists in Sirte, Bani Walid and a handful of towns until Saturday to
surrender or face military force.
But there were indications that fighters were planning to enter Bani Walid, where a powerful tribe is sympathetic to Gadhafi, before the deadline.
National Transitional Council media coordinator Adel Zintani told CNN's Kareem Khadder that fighters could enter Bani Walid by Sunday morning.
"The rebel fighters have surrounded the outskirts of Bani Walid on the western side," he said Saturday.
"Some tribal leaders and many of the residents have surrendered their weapons, but there are still many loyalists who are protecting Moammar Gadhafi and his sons," Zintani said.
The deadline was extended by a week to curb further bloodshed and prevent prevent further destruction, military commanders have said.
"This extension does not mean we are unaware of what Gadhafi's accomplices are up to," Jalil said at a news conference, countering earlier criticism that a grace period might give Gadhafi's forces to regroup.
But Gadhafi's spokesman, who has not been seen since Tripoli fell, said key tribal leaders in Bani Walid remain loyal to the ousted leader.
Musa Ibrahim, in a telephone call from an undisclosed location, told Reuters that the transitional council's messages "are not being heeded here in Bani Walid."
Ibrahim also told Reuters that Gadhafi remained in Libya, though he said he did not know where. He did say Gadhafi was well defended.
Anti-Gadhafi forces are positioning around the former leader's hometown, Sirte, and Bani Walid, said Mustafa Abdul Jalil, chairman of the National Transitional Council, on Saturday.
Ali Tarhouni, interim deputy prime minister and oil minister of the NTC, said the Bani Walid was close to falling.
"It's possible, although we are not sure, that the Bani Walid (tribe) has joined the revolution, and now it's under control of the revolutionaries," he said.
Anti-Gadhafi fighters from the east pushed toward Bani Walid Saturday with virtually no resistance. They were able to reach El Mardum, which sits on the border of Bani Walid province and is home to Khamis Gadhafi's 32nd Brigade base.
The anti-Gadhafi forces entered the base and arrested three men in civilian clothes they claim were loyalists. They also took seven armored personnel carriers.
Tarhouni said Libya's new leadership will move their headquarters from Benghazi to Tripoli this week to begin implementing political plans to shape a new future.
But for the time being, guns trump government on the streets of the capital.
Tripoli has become a city of checkpoints, weapons and no real authority as the threat of Gadhafi's loyalists lingers.
Jittery and suspicious anti-Gadhafi fighters blocked a road Saturday where a drive-by shooting occurred earlier. They collected weapons and registered them at police stations. Those who called themselves rebels just a week ago were now working with Tripoli's law enforcement authorities.
With Gadhafi's armories emptied, guns -- always in large supply in Libya -- have proliferated on the streets.
Those who want to carry weapons now must be issued identification cards, but the selection process is not centralized -- neighborhood councils are making that decision.
A group called the Tripoli Revolutionary Council is trying to exert control over the city, creating the potential for further conflict with the established National Transitional Council in a volatile situation.
Tarhouni announced Saturday the formation of the Supreme Security Committee, which held its first meeting Friday. Among the priorities for the committee were the protection of public institutions and weapons in Tripoli.
The transitional council, meanwhile, is trying to get Libya's oil-dependent economy going again.
It expects to restart oil production at the Misla and Sarir oil fields in less than two weeks, Tarhouni said.