The Earl and Countess of Wessex exchanged gifts with the Prime Minister of Saint Lucia after they received a red carpet guard of honour on their arrival in the country.
Sophie and Edward on Friday began their seven-day tour of the Caribbean where they are also scheduled to visit two other nations, Antigua and Barbuda and Saint Vincent and the Grenadines, after the 11th hour postponement of the Grenada leg of their trip.
The Platinum Jubilee tour was organised to mark the Queen's 70-year reign, and it comes shortly after the Duke and Duchess of Cambridge were criticised for some elements of their recent Caribbean tour, deemed to hark back to colonial days.
Sophie and Edward presented Prime Minister Philip Pierre with a photograph of themselves and a Jubilee box as a "token of appreciation" when they met him at his residence on Friday evening.
In return, Saint Lucia's PM gave the pair a painting of one of the island's turtles rolled up in a long black tube, and before discovering what the gift inside the tube was, Edward joked: "It's not a fishing rod."
The couple then signed the guest book to complete their first day of engagements.
Before meeting Mr Pierre, Sophie and Edward visited the acting governor general Cyril Errol Melchiades Charles.
On their arrival at Hewanorra International Airport earlier on Friday, the royals were greeted in the sunshine by the deputy prime minister Dr Ernest Hilaire and the aide-de-camp to the governor general, Captain Cyril Saltibus, after they disembarked their British Airways flight.
Sophie, wearing a red dress, joined her husband as they walked down the red carpet to a platform, where Edward stood to receive the guard of honour while the island's police band performed the country's national anthem.
The week-long tour will see Sophie and Edward "meet communities, local entrepreneurs and craftspeople, and young people" as well as athletes training for the Commonwealth Games.
No further details were given for Thursday's postponement of the Grenada leg of the tour.
It is understood that the planning of the royal tour involved discussions between the host countries, royal officials and other parties.
