Prince William on Wednesday urged Britain and Ireland not to be "bound" by their shared "troubled past", during the latest high-profile visit to Dublin by a senior British royal.

The prince's speech, in the middle of a three-day trip to Ireland with his wife Kate, echoed similar words delivered by Queen Elizabeth II in her landmark state visit in 2011.

"It is right that we continue to remember those who suffered as a consequence of our troubled past," William said in a keynote address in the Irish capital attended by Foreign Minister Simon Coveney.

"And whilst many wrongs have been done, it is important that we are not bound by these."

The whole island of Ireland was under British rule until a bloody war for independence between crown forces and Irish republicans ended in 1921.

A treaty split the territory between a British-run Northern Ireland and a "free state" which went on to become the modern Irish republic.

Sectarian violence between pro-British unionists and republicans wanting union with Ireland flared in Northern Ireland in the 1960s, leaving more than 3,000 dead on all sides.

The 1998 Good Friday Agreement ended the three decades of violence that had become known as "The Troubles".

Prince William and Kate visit Ireland
The visit by Prince William and his wife Kate was the first royal visit to Ireland since his grandmother Queen Elizabeth's in 2011. Photo: POOL / Brian Lawless

The queen's subsequent 2011 visit was the first by a British monarch in what is now the Republic of Ireland since her grandfather king George V a century earlier.

The Duke and Duchess of Cambridge followed in her footsteps on Tuesday by visiting the Garden of Remembrance in Dublin, which commemorates those who died fighting for independence.

The couple left a message on a wreath which read: "May we never forget the lessons of history as we continue to build a brighter future together."

In his speech Wednesday, William described the wreath-laying ceremony as "one of the truly profound moments for Catherine and me".

He said: "It was a reminder of the complexity of our shared history, and as my grandmother said during her visit in 2011, 'our islands have experienced more than their fair share of heartache and turbulence'."

William and Kate's visit is at a unique time in Irish politics, just weeks after an election that saw a surge in support for nationalists Sinn Fein, whose flagship policy is Irish reunification.

The royal trip also comes in the wake of Britain's departure from the European Union on January 31, with the border between Northern Ireland and the Irish republic a major issue in the process.

"As we look ahead to some changes in our relationship, we must never forget how far we have come together in recent decades in transforming the relationships across our two islands," Willam said.

Copyright AFP. All rights reserved.