Irish Taoiseach Enda Kenny said Margaret Thatcher was "a formidable leader" who "defined an era in British public life."
He said: "Mrs Thatcher was a formidable political leader who had a significant impact on British, European and world politics. During her 11 years as prime minister, she defined an era in British public life.
"While her period of office came at a challenging time for British-Irish relations, when the violent conflict in Northern Ireland was at its peak, Mrs Thatcher signed the Anglo-Irish Agreement which laid the foundation for improved North-South cooperation and ultimately the Good Friday Agreement.
"I extend my deepest sympathies to her family and the Prime Minister David Cameron."
More top news
Former footballer Frank Worthington has denied he is suffering from Alzheimer's - a day after his daughter said he was.
A list of results for London Mayor and the London Assembly
The Cameroonian international collapsed just seven minutes after coming onto the field, according to reports.