CARLETONVILLE, South Africa (CNN) -- Hundreds of workers from a South African gold mine returned to the surface Thursday morning after power to the mine was restored, following an accident that kept them underground for more than a day, the company operating the mine told CNN.

"I'm happy now because we are out and we are alive," said Granny Makau, one of the miners who was trapped inside Elandstrand New Mine, north of Johannesburg. "No one died so we are happy."

A slow and deliberate rescue operation was underway but it was expected to take until Thursday afternoon before all 3,200 workers would see daylight again. More than a thousand had surfaced by mid morning.

"I thought maybe it would take three days or four days (to get out), but I'm happy now that I'm out and everybody is OK," Makau said.

Harmony Gold Mining Company President Graham Briggs, whose company oversees mining operations there, echoed those sentiments.

"It's really a nice sight to see people come out from underground," he said. "It's always difficult when you've got a situation where you've got people underground and they should be on the surface."

Video footage at the mouth of the mine showed workers in hard hats and overalls, exiting a small secondary shaft in groups of about 75. As each lift surfaced, paramedics were seen offering food, water and medical attention, if necessary. In addition, paramedics have entered the mine and are treating workers waiting to leave.

The workers were trapped in the cavernous mine -- which is built like an underground city complete with trains, trucks and cars -- after broken water pipe knocked out electricity to the mine about 6 a.m. Wednesday (midnight Tuesday ET), shutting down power to the elevators, South Africa's ambassador to the United States, Welile Nhlapo told CNN.

The miners were trapped more than 2 kilometers (1.3 miles) underground, according to Lesiba Sheshoka, a spokesman for the South Africa's National Union of Mineworkers.

They were "quite safe" and were given food and water, Nhlapo said.

"This was a situation where the people were not really in danger, they were underground," Briggs told CNN on Thursday. "They weren't in personal danger at any time ... this is a delay in getting people to surface. It's not really an accident in the sense of an underground accident, in the sense of a falling rock."

Although Sheshoka said he could not speak specifically about the conditions at the Elandstrand mine, he pointed to what he called South Africa's generally poor mine safety record.

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According to an official South African government Web site, 202 workers died in mine accidents in 2005, with another 3,961 suffering injuries.

"We're not proud of those statistics at all," Briggs said, in response to the nationwide numbers. "At Harmony, we have improved over the last three years but we need to keep working at it and keep improving it."

In the past decade mine safety across South Africa has shown improvement.

According to the government's Web site, the 2005 safety numbers were a great improvement from 1995, when 533 miners died and 7,000 were injured.

The government pledges further improvements to reduce those numbers. E-mail to a friend

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