Prince Harry has taken part in a "race" with Olympic 100m champion Usain Bolt during his visit to Jamaica.

Prince Harry sprinted down the track after a false start at the University of the West Indies stadium in Kingston as Mr Bolt jogged after him - laughing.

The prince then lunched with republican Prime Minister Portia Simpson Miller, who greeted him with a hug.

Prince Harry is in Jamaica after visits to Belize and the Bahamas to mark the Queen's Diamond Jubilee.

After racing the-third-in-line to the throne, Mr Bolt, 25, immediately called for a rematch.

The sprinter said: "He cheated, I said we would have a rematch in London 2012 and Harry said 'I'm busy.'"

Analysis This was a light hearted encounter which played to Prince Harry's strengths. It was a clash of unequals, but a meeting of two performers. Prince Harry, once a potential liability, is, for now, an obvious asset to an institution which withers if ignored. With his brother Prince William, Princess Diana's younger son represents the future. They appear comfortable in their own skins. It's hard to imagine their father, Prince Charles owning a pair of trainers - let alone wearing them. Yet, however successful this trip might prove to be - and Prince Harry tends to charm those he meets - it won't change the fundamentals of what may come to pass here. Jamaica's prime minister talks of the Caribbean island being on a long journey from slavery at the hands of the British to now, finally, one day possibly soon, removing the queen and becoming a republic.

He went on to praise the prince saying: "He's cool, very down to earth. When you meet dignitaries you think it will be difficult but he just wanted to laugh - it was an honour and a pleasure to meet him.

"I'm still the fastest man in the world so he has a long way to go."

At Prince Harry's request, Mr Bolt signed a photo of a racehorse the prince has a stake in - named Usain Colt. The horse is owned by Ascot Racecourse and Prince Harry is believed to have joined is Birdcage Racing Club, paying a membership fee for a share of Usain Colt's winnings.

It was a rare occasion for a royal to be questioned in public and Prince Harry told reporters: "I was told I wasn't allowed to talk and nobody would ask me any questions - it's going quite well."

Asked what he thought about Jamaica's world standing, the prince highlighted the country's brain drain to the United States.

"This is a very small country, but it doesn't matter how big you are, if you've got talent use it. Don't go running off to America if you've got a clear talent your country needs."

Prince Harry kissed the prime minister on both cheeks after she gave him a hug on the steps of Devon House, a national heritage site. They then held hands to pose for photos under a portrait of the Queen.

'Take our destiny'

The prime minister has said it is time for her country to "take full charge of our destiny" and replace the Queen as head of state.

Image caption The prince responded to the prime minister's hug by kissing both cheeks

The island achieved independence from Britain in 1962 but Ms Simpson Miller has suggested in a BBC interview that it is time for the Queen to be replaced by a home-grown head of state.

In her interview, the prime minister said her nation had come on a long journey out of slavery and now was the time to take full charge of their destiny and achieve full independence.

She first announced her desire for the Queen to be replaced as Jamaica's head of state with a Jamaican president during her swearing-in ceremony in January.

After lunching with the prime minister, Prince Harry visited Bustamente children's Hospital in Kingston and met Jamaican singing star Shaggy, who has raised £500,000 for the hospital with his Shaggy Makes A Difference Foundation.

Diamond Jubilee Royal tours

Prince Harry's arrival in the capital, Kingston, on Monday was greeted with a 21-gun salute by the Jamaican Defence Force.

The prince inspected a military guard of honour before being introduced to lawmakers and diplomats on the tarmRoyal tours around the world in honour of the Queen mapped ac.

He was then driven in a motorcade to the residence of the governor general, the Queen's representative on the island.

His tour is one of several being made by members of the royal family in 2012 as part of celebrations marking 60 years of his grandmother's reign as monarch.

The prince has written thank you letters to the governor generals of Belize and the Bahamas expressing his enjoyment of the tour so far.

To Belize's Sir Colville Norbert Young, he said: "In only 23 hours, I feel as though I have seen so much of Belize through the thousands of people who lined the way. I am hugely grateful for the very happy memories, and I'm very sad to leave."

Prince Harry referred to the friendliness of the Bahamians and beauty of their islands in a separate message to Sir Arthur Foulkes.

"Sharing Monday morning with 10,000 children and young people was a real treat - thank you for being so much fun and making me smile for two full hours," he said.