The band postponed the start of the European leg of their world tour

In a statement, Richards thanked "the doctors and the beautiful ladies who make painful nights less painful and shorter... many thanks, Kiwis."

Richards, 62, is thought to have fallen out of a tree while on holiday in Fiji.

The guitarist will remain as an outpatient at the hospital in Auckland, returning for regular check-ups.

"I'm pretty much at a loss for words to express my deep gratitude," he said.

"I hope I wasn't too much of a pain in the arse - after all, it was my head that was fixed," added Richards in his statement.

Rumours

The performer underwent brain surgery to relieve pressure from his brain on Monday.

The Rolling Stones have had to postpone the start of the European leg of their world tour, which was due to kick off on 27 May in Barcelona.

No rescheduled dates have been announced yet.

His publicist in New York earlier denied press reports that Richards had had a second brain operation.

"There's a lot of cockamamie stories that just aren't true. He's fine," said Fran Curtis.

Richards was first admitted to the Ascot Hospital late last month after receiving treatment in Fiji.

He was released on 2 May but was readmitted on Sunday after suffering headaches.

It is not known how long Richards will stay in New Zealand for treatment.