Prince William and Kate have enjoyed their visit to Uluru so much they may come back, their guide says.

The ancient heart of Australia welcomed the Duke and Duchess of Cambridge and gave them a special gift – a moment of peace and solitude.

On a day warm in spirit and temperature, Prince William and Kate spent Tuesday afternoon at Uluru in the Northern Territory – the site of William’s first encounter with Australia more than 30 years ago.

At the end of the day, which included a welcome to country ceremony by Anangu traditional owners, they were taken on a special guided walk to the base of the desert monolith.

Anangu man Sammy Wilson took the royals on the Kuniya walk, an easy 1km return journey to the Mutitjulu Waterhole, full from recent rains that have also greened the surrounding desert, at the base of Uluru.

The royals walked the last part of the path to the waterhole alone to spend some time in quiet reflection.

For a handful of minutes, theirs was the desert kingdom.

“It’s nice and peaceful down there, very peaceful,” William said later.

Mr Wilson said his guests enjoyed their tour.

“They said ‘Oh, we might come back,” he said.

The duchess, who started the afternoon in a mauve Roksanda Ilincic dress before changing into a grey and white checked sundress, and William waved to the 50 or so onlookers who had gathered to see the royal couple ahead of their walk.

After the walk, William and Kate enjoyed a sunset viewing of Uluru, watching the rock’s magnificent colour-changing display in the waning sunlight.

The viewing was a late addition to their schedule that was kept under wraps to give the royals a rare moment of intimacy – albeit one still captured by a handful of authorised media and a crowd of wellwishers.

It was their last engagement on a packed afternoon that had hundreds of locals and tourists, some having driven from Alice Springs or further afield, turning out to wish them well.

The couple’s visit began with the future of central Australia, presenting certificates to graduate students at the National Indigenous Training Academy and meeting students from high schools at an afternoon tea, before ending with their immersion in the Red Centre’s ancient traditions.

Anangu elders danced an “inma” – a song and story – in the red desert dust at a welcome to country ceremony at the Uluru-Kata Tjuta Cultural Centre where the royals were also presented with gifts.

Among Kate’s gifts was a necklace of painted gumnuts and red ininti seeds from the local desert.

Although he remained behind in Canberra, baby Prince George was given a gift of hand carved wooden animals – said to be ideal for the royal sandpit.

William was given a hand-carved shield, after being presented with a barbed hunting spear made of mulga wood and kangaroo tendon bindings earlier in the day.

It was the first visit for the young royal family but a return for William, whose journey to the Red Centre as a babe in arms in 1983 is looked on warmly by the Anangu people and Territorians alike.

Cecilia Cadell met the royals on the Kuniya walk and said hello.

“She was beautiful – she said hello, it makes you have goosebumps,” she said.

Melbourne visitor James Bremner, who watched the media pack at the Uluru visit, pitied the royals.

“I feel sorry for them, in a way, that the can’t have a normal life as such,” he said.

William and Kate will spend the night – their first away from George in Australia – at the exclusive Longitude 131 resort, situated in the desert close to Uluru.

The resort’s 15 luxury tent pavilions feature king-sized beds, prestige bathrooms and sweeping private views of Uluru.

On Wednesday the couple fly to Adelaide, where they will visit Elizabeth, named after William’s grandmother, the Queen.