LONDON — Queen Elizabeth II wrapped up her groundbreaking four-day visit to the Irish Republic on Friday, a trip that ranked among the most politically freighted of her almost 60 years on the throne.

While the queen has no formal political power, her visit — the first by a British monarch — offered powerful symbols of reconciliation and drew broad acclaim among Irish politicians. Her status both as head of state and as the most respected member of Britain’s royal family was taken by her hosts as imparting a particular gravity to her words, sealing a closeness that has grown in recent years. Virtually every word and gesture — down to wearing Ireland’s distinctive emerald green when she arrived — seemed to have been weighed in advance to avoid any impression of royal hauteur.

“Together we have much to celebrate,” the queen said in a keynote address at a banquet in Dublin on Wednesday night, referring to “the ties between our people, the shared values and the economic, business and cultural links that make us so much more than just neighbors, that make us firm friends and equal partners.”

It was at the official dinner that the queen spoke the words that have been taken as the central message of her trip. “To all those who have suffered as a consequence of our troubled past, I extend my sincere thoughts and deep sympathy,” she said. “With the benefit of historical hindsight, we can all see things which we would wish had been done differently or not at all.”...