The Queen has wrapped up her landmark four-day state visit to Ireland, which analysts said had exceeded expectations and put Anglo-Irish relations on a new footing, according to a report from the ABC (21/5) drawing on Agence  France Presse.

Describing the visit as one of the most significant and groundbreaking visits of her near 60-year reign, the ABC said Her Majesty faced thorny historical issues head-on and won praise for doing so.

Queen Elizabeth II even ended her heavily policed trip with an impromptu walkabout in the second city of Cork, underlining the extent to which old wounds had been healed and cynics won over.

A tour of the medieval Rock of Cashel monument also saw a first handshake between the British monarch and an official from hardline republicans Sinn Fein, the political wing of the IRA and vocal opponents of the trip.

It was the first visit to the Republic of Ireland by a British sovereign since it won independence from London in 1922.

Irish prime minister Enda Kenny invited the Queen to pay a return visit as he said goodbye to her at Cork airport as she boarded her plane.

"At the bottom of the steps I said to her, 'And your majesty, would you like to come back again sometime'.

And she said, 'Yes, I would very much like to do that,'" Mr Kenny told RTE state radio.

"So, at sometime in the future, you may see her return."

…Surpassed expectations….

Patrick Geoghegan, a senior history lecturer at Dublin's Trinity College, said the visit had surpassed his expectations.

"It was really only when watching the speeches in Dublin Castle that it really brought home to me how historic and just how important an event the visit has been," he said.

It now seemed "hard to believe" that the Republic of Ireland had never before had a state visit from across its only border.

"The fact that we have now done that means both countries can move with confidence, so I think it has been an extraordinarily successful visit," Geoghegan said.

"Even people who were cynical at the start of the week were moved and touched by the visit by the end of the week."

Michael Anderson, a research fellow at University College Dublin, said people had been "astonished" by the "sincerity and dignity" shown by the Queen.

The fact the British monarch began her speech in Irish – which had a stunned president Mary McAleese repeatedly mouthing "wow" – held "incredible significance" and symbolised the big impact of small gestures, he said.

"This was a genuine reconciliation of something that went on for 800 to 900 years."….

Even Sinn Fein president Gerry Adams praised the speech.

"I hope some good will come from this visit and I particularly was taken by Queen Elizabeth's sincere expression of sympathy to all those who had suffered," he told the BBC.

Threats from dissident republicans opposed to the peace process in British-ruled Northern Ireland and an early rash of bomb alerts failed to overshadow the visit.