The Taoiseach, Bertie Ahern, rejected suggestions that Mary Harney's resignation would cause problems for the Government.
However, he said that while he had an understanding with Ms Harney that the Government would run its full term, obviously he had no such understanding with whoever would take over from her.
He said that if he did not get that commitment, that would leave him in a different position.
Green Party leader Trevor Sargent said Ms Harney's resignation introduces a 'huge instability' into the Government.
He added that the Taoiseach might have to reassess his preferred election date because his coalition partner appeared to be 'cannibalising itself' and there was no certainty he would have the numbers.
Deputy Sargent said he personally wished Ms Harney well in her future career, but added that she had had a good innings.
Labour Party leader Pat Rabbitte said he did not believe it credible for the Government to go on as if nothing has happened.
He said Mary Harney's departure leaves a dysfunctional minor partner in government.
In a warm tribute, Fine Gael leader Enda Kenny said he had known the Tánaiste for many years and over that time he had known her as a politician of integrity and honesty.
The Sinn Féin leader in the Dáil, Caoimghín Ó Caoláin, said the Fianna Fáil/PD Government is 'at the end of the line'. And he said 'the whole lot of them should now resign and call a General Election'.
The EU Internal Markets Commissioner, Charlie McCreevy, said Mary Harney has been one of the outstanding politicians of her generation.
He said that since entering public life nearly thirty years ago she has been consistent, courageous and determined in advocating the distinctive economic and social policies in which she passionately believes.
He said that although they differed on some issues and occasionally fought tough political battles in private, Ms Harney has been consistently loyal and trustworthy and remains among his closest and most valued friends.
