Irish president Michael D Higgins said Margaret Thatcher's place in history has been secured as Britain's first female prime minister.
President Higgins led the condolences on Mrs Thatcher's death from the Republic.
The President said she will be remembered as one of the most conviction-driven British prime ministers.
"The policies of Mrs Thatcher's government in regard to Northern Ireland gave rise to considerable debate at the time.
"However, her key role in signing the Anglo-Irish Agreement will be recalled as a valuable early contribution to the search for peace and political stability," he said.
Taoiseach Enda Kenny described Mrs Thatcher as a "formidable political leader" who 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," he said.
Tanaiste Eamon Gilmore said he had extended his sympathy to Foreign Secretary William Hague and Northern Ireland Secretary of State Theresa Villiers. Fianna Fail leader Micheal Martin said discussion of Mrs Thatcher's political legacy had to take a "balanced account" of her approach to Irish affairs.
"While I or the Fianna Fail party would have had little in common with the politics of Mrs Thatcher, it would be wrong not to acknowledge that the long journey towards the peace, took its first faltering steps in the bilateral discussions between Mrs Thatcher and Charles Haughey," he said.
But former Taoiseach Bertie Ahern said he believed "nothing was achieved" towards peace during Margaret Thatcher's time as prime minister. "As De Valera said about Churchill, she was good for the UK, but her policies were not good for Ireland," he added.
"She was a unique lady and a formidable lady. She was prime minister for the same length of time that I was Taoiseach," he said.
Sinn Fein leader Gerry Adams attacked Margaret Thatcher for the "great hurt" she did to the Irish and British people during her time as British prime minister.
Mr Adams listed what he believed she had done wrong, including her "shameful role" in the hunger strikes of the early 1980s. "Her Irish policy failed miserably," he said.