CARLETONVILLE, South Africa — More than 2,000 trapped gold miners in South Africa were rescued in a dramatic all-night operation, and efforts gathered speed Thursday to bring hundreds more to the surface.

There were no casualties when a pressurized air pipe snapped at the mine near Johannesburg and tumbled down a shaft Wednesday, causing extensive damage to an elevator and stranding more than 3,000 miners more than a mile underground.

The mine owner and South Africa’s minerals and energy minister vowed to improve safety in one of the country’s most important industries.

Earlier hopes that all the miners would be rescued by lunchtime faded and company officials said it would more likely be early evening.

“We nearly died down there,” one man yelled as he walked past reporters. “I’d rather leave (the job) than die in the mine.”

The trapped workers were bringing brought to the surface in a second, smaller cage in another shaft. Most of the miners who emerged into the blinding sunlight looked dazed and exhausted, but there were no signs of injury — although one apparently dehydrated man rode away in an ambulance.

One large group emerged from the shaft singing traditional songs and stamping their feet with joy despite their exhaustion. They were greeted by a crowd of ululating women miners.

The hundreds of workers who remained underground were all near a ventilation shaft and had been given water — although no food for fear of provoking a scramble among hungry miners, a health and safety chairman for the National Mineworkers Union, Peter Bailey, said.

The accident prompted allegations of the industry cutting safety corners in the name of profit — and accusations from the government that mine owner Harmony Gold Mining Co. did not bother to inform it of the potentially devastating crisis.

The minister of Minerals and Energy, Buyelwa Sonjica, complained that she learned about the early morning accident from the late evening news. She said President Mbeki also found out from the news bulletin.

Ms. Sonjica said during a visit to the Elandsrand mine at Carletonville — a town in South Africa’s mining heartland near Johannesburg — that health and safety legislation would be “tightened up.”

Last year, 199 mineworkers died in accidents, mostly rock falls, the government’s Mine Health and Safety Council reported in September. One worker was killed last week in a mine adjacent to Elandsrand.

“We have to recommit ourselves to refocus on safety in this country; our safety record both as a company and an industry leave much to be desired,” the chairman of Harmony Gold Mining Co., Patrice Motsepe, said according to the South African Press Association, as union officials accused the industry of taking short cuts on safety in the interest of profit.

Harmony’s per-share price on the Johannesburg Stock Exchange dropped almost 5% Friday morning, but later recovered and was at $10.99 Thursday afternoon, only slightly off the previous day. JPMorgan analyst Allan Cooke said the accident would hurt Harmony’s earnings, especially if the shaft remains closed for the entire quarter.

As rescuers slowly brought the miners to the surface Thursday, family members stood outside the mine offices, complaining that they had not been given enough information about their loved ones.

“I am very traumatized, exhausted, not knowing what is going on,” Sam Ramohanoe, whose wife, Flora, 31, was among the trapped, said. “It is very unfair to us, not knowing what is going one with our beloved ones.”

Sethiri Thibile, who was in the first batch of miners rescued about 19 hours after the accident, held a cold beef sandwich and a bottle of water he was given when he reached the surface.

“I was hungry, though we were all hungry,” Mr. Thibile, 32 said. He said there was no food or water in the mine.

“Most of the people are scared and we also have some women miners there underground,” Mr. Thibile said.

A regional chairman for the union, Deon Boqwana, said officials were in contact with the miners below ground by a telephone line. Mr. Boqwana said the smaller cage being used to bring miners out can hold about 75 miners at a time. He said it normally takes three minutes to reach the surface but would be slower because rescuers were being careful.

A spokesman for the union, Lesiba Seshoka, said that the mine was not properly maintained.

“Our guys there tell us that they have raised concerns about the whole issue of maintenance of shafts with the mine (managers) but they have not been attended to,” he said.

A company spokeswoman, Amelia Soares, said the mine had won a number of safety awards and had never seen any fatal accidents. She said the company was likely to suffer considerable loss in output during the closure, but was unable to give a precise estimate, saying that attention for now was concentrated on the rescue operation.