The Queen woke to find herself an unlikely star in the Irish Republic on Thursday, almost universally praised for her gestures of reconciliation during the first official visit by a British monarch in 100 years.

Her words and bearing have astonished and delighted many. Both the Queen's speech at the state dinner in Dublin Castle and her silent tribute at the national garden of remembrance to those killed fighting the British for Irish independence at the start of her visit on Tuesday have been well received. There has even been speculation that her visit may outshine Barack Obama's next week.

Eamon Gilmore, the tánaiste (Ireland's deputy prime minister) and foreign minister, told the Guardian: "The visit has gone very, very well and has been great for the country."

The broadcaster RTÉ said 500,000 viewers watched its coverage of the Queen planting a tree at the presidential residence on Tuesday, and other channels also covered the occasion.

Even her few words of Gaelic at the start of her speech at the state dinner on Wednesday evening – "A Úachtárain agus a chairde" ("president and friends", immaculately pronounced) – were an unexpected gesture. Mary McAleese, the Irish president, who was sitting beside the Queen, turned to others at the table open-mouthed, exclaiming "wow".

The speech, with its apology for "things we wish had been done differently or not at all", was greeted across the Irish political spectrum with near universal praise.

Her words, calling for forbearance and conciliation and the loosening of the knots of history, striving to create a more harmonious relationship "close as good neighbours should always be", led all the Irish papers.

All were full of praise for the address, which was delivered in front of dignitaries from both sides of the Irish border, including the taoiseach Enda Kenny, the Unionist first minister of Northern Ireland Peter Robinson, religious leaders including Cardinal Seán Brady, the Nobel laureate Seamus Heaney, Irish rugby star Brian O'Driscoll and various Irish former prime ministers. They gave the Queen rapturous applause and a standing ovation.

Some Sinn Féin politicians pronounced themselves "underwhelmed" – and found themselves roundly attacked.

The television interviewer Vincent Browne asked the parliamentarian Aengus Ó Snodaigh: "So when did the IRA ever apologise?"

The Sinn Féin president, Gerry Adams, however, united with David Cameron to praise the Queen's historic address. "I believe that her expression of sincere sympathy for those who have suffered as a consequence of our troubled past is genuine," he said.

His party has been criticised for refusing to meet the Queen.

Cameron said she had shown enormous sensitivity to past issues and problems, as well as the opportunities for the future. "I think this visit will set the seal on what is already a very strong relationship between our two countries, but a relationship I believe that can get even stronger still."

The Queen and the Duke of Edinburgh moved away from the symbolism of the first half of their visit, to what was undoubtedly more congenial and relaxed ground for her, visiting several stud farms on the Curragh near Dublin.

At the Irish National Stud at Kildare the Queen was applauded as, visibly relaxed and smiling broadly, she was introduced to jockeys, trainers, farriers and apprentices and shown racehorses. Sue Lilley, farrier course co-ordinator, said: "This is the biggest day of our lives."

Simon Coveney, the Irish agriculture minister, who accompanied the royal party, said: "I think she is on comfortable ground here, surrounded by horsey people, many of whom she knows. She would be welcome to come to the races here at any time."

Michael O'Connell, the Labour lord mayor of Cork, called on residents to line the route when the Queen visits the city. It is yet another resonant gesture, as one of O'Connell's predecessors, Terence MacSwiney, famously starved himself to death in Brixton prison in 1920 after being jailed by the British for sedition.

O'Connell said the visit was "a unique opportunity for the people of Cork, civic leaders and businesses to show the best of what our special city has to offer and to make an unforgettable first impression.

"It's our opportunity to give Queen Elizabeth a welcome to remember in front of an audience of over 30 million people tuned in worldwide."

In Dublin, the British embassy hosted a reception to mark the visit, with a fashion show featuring Irish and British designers, followed by a concert featuring the boy band Westlife, the X Factor finalist Mary Byrne, who was born locally, and the 1996 Irish Eurovision song contest winner Eimear Quinn.

Later, the Queen was given a five-minute standing ovation as she went on to the stage to meet performers after a gala concert at the Dublin Conference Centre.

Members of the 2,000-strong audience cheered and whistled as the monarch waved back enthusiastically at the overwhelming response.

It was the first time members of the Irish public had been able fully to show their support for the Queen's decision to pay her first State visit, and the crowd inside the venue remained on their feet clapping her for the entire time she was on the stage meeting acts.

Gay Byrne, the TV personality who compered the evening, told the audience: "You were present at an historic occasion. Remember it."

When the Queen arrived inside the auditorium she was given a warm reception, before Byrne said: "I never dreamed I would live to see this day."

Obama will be visiting County Offaly to see his ancestral family roots, before a state visit to London when he will meet the 85-year-old woman who has unexpectedly become an Irish media star.

Press Reaction: 'Not just polite applause'

The Irish newspapers have covered the Queen's visit in exhaustive detail, from the constitutional and political implications to details of the state dinner and Her Majesty's clothes – and all have been lavish in their praise of the 85-year-old monarch.

The Evening Herald: "You really could not make it up … It was truly a spectacle of epic proportions. When Queen Elizabeth rose to speak at last night's state dinner in Dublin Castle, stylish in a white silk crepe state dress and the Queen Mary tiara, she had a little surprise up that shamrock-embroidered sleeve. In a strong voice that belied her 85 years she began with the words "A Uachtaráin agus a chairde".

Irish Independent: "It was a moving speech delivered in her clear cut crystal voice and after the toast the room stood and applauded. Not just polite applause but sustained heartfelt appreciation of the bridge that the Queen herself had built … she had the look of a woman for whom the weight of history had just got a lot lighter."

Irish Times: "For some, perhaps far fewer in number than was the case on Monday … Queen Elizabeth should simply have apologised for colonial rule, or never have come at all. As expected, she was far more nuanced … Queen Elizabeth is welcome as a remarkable woman in her own right, as a figure to whom a significant minority on this island give allegiance and, above all, as a symbol of the mutual affection and common interests of two separate but closely connected countries."