Libyan rebels backed by powerful Nato air strikes fought their way into parts of the government-held oil town of Brega on Monday in one of their most ambitious offensives of the war so far.

The attack, launched on Thursday, has seen rebel units push towards the town from the east, north, and south, with house-to-house fighting reported by Radio Misrata in New Brega, a dormitory suburb 18 miles east of the main town.

Rebel units are being aided by some of the most sustained Nato bombing yet seen, amid claims that forces loyal to Muammar Gaddafi were retreating west towards the town of Ras Lanuf.

Nato reported 32 military vehicles, including tanks, rocket launchers and armoured personnel carriers, destroyed in three days of intensive air strikes.

The use of alliance warplanes in what amounts to a combat support role, rather than protection of civilians, is likely to sharpen criticism from some quarters that Nato is overstepping its mandate.

The bombing is clearly having an effect. Rebel infantry units have made steady advances in five days of fighting, picking their way through minefields and trenches filled with corrosive chemicals in the face of only patchy resistance by regime forces.

Still, how far the rebels have advanced remains unclear, with some commanders claiming Brega is poised to fall and others predicting more fighting ahead. Neither the rebels nor the government have issued comprehensive casualty figures.

Some leaders in the rebel capital, Benghazi, insist troops have captured much of the Old Town and oil depot, with less than 200 government troops holed up in an industrial park without food or water. But one rebel political source told the Guardian it was not yet clear whether rebel units had entered Brega proper or only New Brega.

The source, who wished to remain anonymous, said rebel intelligence indicated that government troops may have pulled back to the village of Bishir, from where Grad rockets are being fired at rebel units, indicating that more fighting may lie ahead before rebels can claim victory.

Yet after months of failure, Libya's opposition appears to be solving chronic command and logistics problems that hampered operations in the early part of the war. Rebel units twice captured Brega in the spring only to lose it again to government counter-attacks.

The southern rebel attack has reportedly swung around behind the town, preventing government forces from sending reinforcements along the coast road.

Brega's capture would deprive the Gaddafi regime of one of Libya's most important oil installations.

"When you control this [Brega oil terminal] it means Gaddafi has nothing," said rebel spokesman Mohammed Durat in Misrata. "When he loses Brega it will be very important."

For the rebels, it would be a psychological boost after many weeks of stalemate and failed attacks.

Nato also said on Monday that it had destroyed the radar antennas at Tripoli international airport, claiming they were being used for military purposes.

In a related development, David Cameron had a public disagreement with South African president Jacob Zuma in a meeting in Pretoria. Zuma pushed for Nato to give talks with Gaddafi a chance to succeed but Cameron said the Libyan leader must first step down. "We both want to see a future for Libya that doesn't include Colonel Gaddafi," Cameron said. "The difference is that the president sees that as the outcome of a political process, whereas I believe for a political process to work it has to be the starting point. That is the difference between us. That's the gap."

Russia, meanwhile, criticised the US and other countries on Monday for recognising the Benghazi-based rebel leadership as the legitimate government of Libya, saying they were taking sides in the rebellion to oust Gaddafi. "Those who declare recognition stand fully on the side of one political force in a civil war," foreign minister Sergei Lavrov told reporters.

US secretary of state Hillary Clinton announced broad recognition of the rebels on Friday during a meeting of the international contact group on Libya in Istanbul. The US, Britain and France have taken a hawkish line on Gaddafi but Russia and China are critical of Nato's policy and both boycotted the contact group meeting.

In a speech on Saturday Gaddafi described the rebels as traitors and rejected suggestions he was to leave the country.