AUCKLAND, Jan 22 (Reuters) - Thousands of people gathered in parks, halls and churches around New Zealand on Tuesday as the country buried Sir Edmund Hillary, the conqueror of Mount Everest.

The state funeral of the first man to reach the summit of the world's highest mountain was, in keeping with the man himself, modest, with 600 family, friends and dignitaries in the church.

Hillary's coffin was draped in the New Zealand flag, cream-coloured Nepali prayer scarves, and Hillary's climbing axe.

"We mourn as a nation because we know we're saying goodbye to a friend," Prime Minister Helen Clark told the service.

Among those attending were the son of Tenzing Norgay, the Nepali sherpa who accompanied Hillary to Everest's 8,850 metre (29,035 feet) summit.

Thousands, young and old, had filed past the coffin in the previous 24 hours to pay their last respects to the former beekeeper, adventurer, and humanitarian, who died at the age of 88 on Jan. 11 after a heart attack.

On Tuesday, mourners around the country gathered at giant video screens to watch the service, which was also televised in Nepal and at New Zealand's Scott Base in Antarctica, which Hillary founded.

After scaling Everest, Hillary led a number of expeditions. In 1958, he and four companions travelled overland in three modified tractors to become the first to reach the South Pole by vehicle.

"Adventure was compulsory in the Hillary family," Hillary's son Peter told the service. "We always feared where dad was going to take us in the upcoming school holidays."

"That shared adventure was one of the greatest gifts he gave to his family and friends," he said. Peter Hillary followed in his father's footsteps and became a mountaineer.

After the service Hillary was to be cremated in a private family ceremony. He had asked that his ashes be scattered on Auckland's harbour. (Writing by Gyles Beckford; Editing by Michael Perry and Alex Richardson)

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