(Adds details, CEO quotes)

By James Macharia

ELANDSRAND MINE, South Africa, Oct 4 (Reuters) - The first 75 miners out of 3,200 trapped deep underground in a South African gold mine were brought to the surface early on Thursday, a senior mine official said.

Harmony Gold <HARJ.J> is confident it will rescue all the other miners trapped since Wednesday morning at the mine near Carletonville, southwest of Johannesburg, Chief Executive Officer Graham Briggs told Reuters.

"There have been no injuries or deaths ... It may take as long as 10 hours, the cage (lift) is travelling fairly slowly to avoid risks ...I 'm very confident all will come out," Briggs said.

The miners at the Elandsrand mine were caught about 2.2 km (1.4 miles) below ground when a power cable to a lift broke at around 0800 GMT on Wednesday, a spokeswoman for Harmony -- the world's fifth biggest gold producer -- said earlier.

A National Union of Mineworkers (NUM) spokesman said the miners were trapped in a cramped space where temperatures could reach 30 to 40 degrees Celsius (86-104 Fahrenheit).

Briggs said rescuers on the surface were in contact with the trapped miners and clean air and water were being pumped down to them.

"It's a very serious incident, but it's under control," he added.

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