The head of the Transitional National Council said Saturday that Libyan fighters had surrounded key loyalist-controlled cities where many believe Moammar Gaddafi and three of his sons could be holed up, waiting for a showdown.

The council has extended until Sept. 10 a deadline for Sirte, Bani Walid, Jufra and the desert city of Sabha to surrender or face a military onslaught. Military commanders have said they want to allow time for negotiations to work before undertaking a battle that could entail significant bloodshed.

“With God’s grace, we are in a position of strength right now. We can enter any city,” said Mustafa Abdel Jalil, speaking at a news conference in the anti-Gaddafi stronghold of Benghazi. “Our military and our forces will move militarily to surround these cities. . . . This is an opportunity for these cities to announce their peaceful joining of the revolution.”

The council, which has been attempting to provide humanitarian aid to the city of Sirte and others, said negotiations were informal at this point and being obstructed by Gaddafi loyalists. Sirte is Gaddafi’s home town and last coastal stronghold, as well as a power base for his tribe, the Gaddafa. Although the tribe is not the largest in the city, its members are armed and more powerful than the others, said Shamsiddin Ben-Ali, a spokesman for the council.

Sirte, which Gaddafi declared the capital of resistance in an audio statement Thursday, is now surrounded on all sides, Ben-Ali said. Electricity has been restored to the city after being cut off for days, he said.

NATO has focused its firepower on Sirte since the capital fell into the hands of Libyan opposition fighters last month. But it has also begun to shift its attention to Bani Walid, a desert town 104 miles southeast of Tripoli where rebel commanders believe three of Gaddafi’s sons — Saif al-Islam; Mutassim, the former national security adviser; and Saadi, a former professional soccer player — may be hiding. Some suspect the leader himself may be there.

Abdel Jalil, the council head, said that the council had no plans to disarm or remove fighters from Tripoli while Libya was still not completely “free” from Gaddafi and his followers.

On Friday, thousands of men, women and children briefly reclaimed Tripoli’s main square for the largest celebration in the city since Gaddafi’s forces were chased out just over a week ago.

Security concerns and the presence of excited young fighters firing guns into the air had discouraged some families. But on Friday, Martyrs’ Square, as the former Green Square is now known, was the scene of intense celebrations, with children holding balloons and flags in the rebel colors of red, black and green.

“You can’t imagine how happy we are,” said Amina Balaban, an English teacher who was there with her husband and children. “We never came to celebrate here before.”

But while the crowds shouted slogans celebrating their freedom and Gaddafi’s downfall, many said the job would not be done until he was caught. Late Friday, the young gunmen returned to the square to fire their weapons.

The whereabouts of Gaddafi remain the subject of intense speculation, with reports placing him anywhere from the Algerian border to Tripoli itself.

After Gaddafi’s audio statement Thursday, Abdul Basset Haroun al-Shahaidi, a top commander in the rebel’s state security services, said he believed Gaddafi was in Sirte.

Shahaidi said he and other commanders have almost daily meetings with NATO representatives to plan the assault on Sirte. About 70 percent of their intelligence comes from NATO observations from the sky, he said, and the rest they gather with clandestine contacts inside the city.

“This will be a big, big fight, not like Tripoli,” he said. “We don’t know exactly what [Gaddafi] has inside. Before, in Tripoli, he said he had guns and chemical weapons and we went slowly and took it step by step.”

In Benghazi, Abdel Jalil returned from Paris on Friday and announced that the Transitional National Council would move to the capital next week.

“Tripoli is the permanent capital of Libya,” Abdel Jalil said, adding that the capital “deserves” the council’s presence.

In Tripoli, rebels acknowledged differences of opinion between civilian and military leaders and between pro-Western officials and Islamist forces. But they said the tensions were manageable.

“I can guarantee this is a safe city, and the tensions, to us, are normal,” said Abdulrahim el-Keib, a member of the transitional council for Tripoli. “We do have a vision for a bright future for Libya, and a safe one.”

Denyer reported from Tripoli.