Prince William and Kate Middleton kicked off a four-day royal visit to Sweden and Norway with a lavish luncheon with the Swedish royal family and by hitting the ice in a Stockholm park.

The British royal couple, who are expecting their third child in April, dined with King Carl KVI Gustaf and Queen Silvia, as well as Crown Princess Victoria and her husband Prince Daniel, on Wednesday morning (AEDT) after challenging each other to a light-hearted game of the Nordic sport, bandy.

Bandy is similar to ice hockey, but played with a small ball instead of a puck and with larger pitches and goals.

After a brief tutorial on the sport, William and Kate faced off in a penalty shoot-out, with William scoring two goals in a three-shot game to Kate’s one.

The Duchess takes a shot at goal! 🏒#RoyalVisitSweden pic.twitter.com/FNjaZrlU6P

— The Prince and Princess of Wales (@KensingtonRoyal) January 30, 2018

The duke and duchess, accompanied by Crown Princess Victoria and Prince Daniel also visited the Royal Palace of Stockholm, where they joined the Swedish royal family for a rare photo opportunity.

Kate is seen showing off her growing baby bump in a forest green dress in one of the palace’s stunning drawing rooms.

Following the luncheon, William and Kate walked through the picturesque cobbled streets of Stockholm and the city’s oldest public square, Stortorget Square, to the Nobel Museum.

They attended Sweden’s national centre for architecture and design, ArkDes, for an event celebrating Sweden’s most iconic global designers, including Ikea, and some of the country’s up-and-coming homeware designers.

Later in the evening, William and Kate attended a black-tie dinner with Swedish Prime Minister Stefan Löfven and his wife Ulla Löfven at the Residence of the British Ambassador.

The Duke and Duchess meet Swedish Prime Minister Stefan Löfven and his wife Ulla Löfven at the Residence of the British Ambassador #RoyalVisitSweden pic.twitter.com/hEKzxT6TTM

— The Prince and Princess of Wales (@KensingtonRoyal) January 30, 2018

As well as meetings with the royal families of Sweden and Norway and political leaders in the Nordic countries, the royal couple’s agenda also includes briefings about the military forces in the region.

William – second-in-line to the throne – served in Britain’s armed forces from 2006 until 2013, and worked as a search and rescue helicopter pilot before he started last year to focus full-time on his royal duties.

Also on the agenda is a visit to the Karolinska Institute where they will be learning about how Sweden is tackling mental health issues among young people.

Kate, William and his brother Harry have made campaigning about mental health a priority, with the brothers speaking about how the death of their mother Diana, Princess of Wales, in a 1997 car crash had left them with deep emotional scars.

Britain’s monarchy has ridden a wave of public support in recent years due to the popularity of William, Kate and Harry.

– with AAP