Colonel Muammar Gaddafi has offered to enter talks with the Libyan rebels over the formation of a transitional government as loyalist fighters are pushed further to the outskirts of Tripoli and rebel forces prepare for an assault on the ousted dictator's hometown of Sirte.

Moussa Ibrahim, regime spokesman, called the New York office of the Associated Press on Saturday night and said Gaddafi wanted his son Saadi to lead talks with the National Transitional Council. Ibrahim, who was identified only by his voice, has proved one of the despot's most loyal and vocal allies as the 42-year-old regime crumbles. He said he was still in Tripoli, while Gaddafi – whom the rebels and Nato are desperately trying to capture – remained in Libya.

The offer of negotiations were slapped down quickly by a senior NTC official, who said the rebels would not talk to Gaddafi unless he surrendered.

"No negotiation is taking place with Gaddafi," said Ali Tarhouni, the rebel official in charge of oil and financial matters. He told Reuters: "If he wants to surrender, then we will negotiate and we will capture him."

Guma el-Gamaty, the UK co-ordinator of the NTC, said the rebels were "absolutely 100% not" prepared to enter into negotiations with Gaddafi about a transitional government.

He said: "The only negotiation is how to apprehend him, [for him] to tell us where he is and what conditions he wants for his apprehension: whether he wants to be kept in a single cell or shared cell or whether he wants to have his own shower or not, you know. These are the kind of negotitations we are willing to talk about."

The British foreign secretary, William Hague, said on Sunday there had never been any possibility of the Libyan dictator being part of a transition. He described Gaddafi's apparent offer of talks as "delusional".

"I referred a few days ago to Colonel Gaddafi making delusional statements and this is another one of them," he told the BBC.

"A transition of power is already taking place. The NTC ministers are in Tripoli and in increasing control of the situation. What is needed from the remnants of the Gaddafi regime is the fighting to stop."

Speculation over the political future of Libya came as the search for Gaddafi and his sons continued, with the rebels fighting for control of a major supply road to the capital on Saturday after seizing a border crossing with Tunisia.

The Egyptian news agency Mena, quoting unidentified rebel fighters, reported from Tripoli that six armoured Mercedes sedans had crossed the border at the south-western Libyan town of Ghadames into Algeria. The report said that the cars could be carrying top figures from the Gaddafi regime. Rebels were unable to pursue the vehicles because they did not have ammunition or the necessary equipment, Mena said. The report could not be independently confirmed.

Clearing the supply road of remaining Gaddafi loyalists from the Tunisian border to Tripoli would help to ease growing shortages of fuel and food, particularly in the battle-scarred capital, where problems are now acute.

Rebel officials in Tripoli are struggling to maintain electricity and water supplies. The NTC announced on Saturday that a new Tripoli local council would be operating from the previous municipal building and launching a website with updates on basic services.

On Sunday, a ferry chartered by the International Organisation for Migration is due to take aboard 1,200 stranded foreigners and leave Tripoli harbour.

Usama el-Abed, deputy chairman of the Tripoli council, said: "Definitely we recognise there are a lot of challenges. The basic services are the ones we are concentrating on now – the health sector with regard to hospitals, staff, medication."

In the city, neighbourhoods have been without running water for several days and the electricity station is no longer coping with demand. Rebel officials who are gradually taking over the running of the capital say there has been no damage to water or power supply lines and are instead blaming the deterioration on "technical issues".

The shortages underscore the urgency of restoring essential services in a city that enjoyed guaranteed running water and power under Gaddafi. Mahmoud Shammam, information minister in the NTC, said it already controlled most of the supply road, but that regime loyalists were shelling it in the area of Zwara, west of Tripoli. "We hope to be able to control the road today," he told reporters.

Leaders of the council know that they will be judged by whether they can match the benchmark set by the ousted autocrat and are stressing that essential supplies, including drinking water and petrol, are on the way.

"We don't know the electricity problem, we don't know the water problem, we don't know the communication problem," Shammam said. "In the next few days we will have answers."

Dozens of decomposing bodies still lie in and around the main hospital in the Abu Salim district, abandoned by medical staff during the fighting, according to Reuters. El-Abed insisted: "We have a team working on that today. Some of these issues will be in relation with the Red Cross."

Pressed on whether the city was now under full rebel control, he replied: "The Gaddafi regime forces have definitely come to their end, but there will always be remnants, there will always be residues, there will always be people who, for the sake of vendettas and vengeance and stealing the joy of celebration, will come up with some action that may not be expected."

Shammam added that a stabilisation taskforce had been set up to work with other teams in restoring essential services. "We have 30,000 metric tonnes of gasoline and will start distributing to the public today. Diesel fuel will arrive the day after tomorrow, which is essential to the city to support the power and water supply."

With all the city's petrol filling stations remaining closed, drivers are paying blackmarket rates of about $80 (£50) for 20 litres of petrol. The two mobile telephone networks are also working intermittently in another indication of a wobbling infrastructure.

More pressing for many residents, however, is the stench from growing piles of refuse, which is being heaped on to main roads. Tripoli's council has not yet sent out rubbish trucks to collect rubbish. However, one lone truck – driven by a council worker who had not been asked to do so – was collecting rubbish from the Tajura area on Friday. "These are my people and I will look after them," he said, as he heaped one week of putrid waste into his truck. "If all the people work together, none of us will have problems."

NTC officials said they did not yet know how many people were affected by power and water shortages and would try to issue an assessment on Sunday.

One source said: "It's not a crisis yet, but it might become one. It's certainly a concern."