The Fine Gael leader Enda Kenny tonight wished Pope Benedict XVI well and urged him to would visit Ireland early in his papacy.
"I wish the new Pope Benedict XVI every success in his new role as head of the Roman Catholic Church. He will need his considerable intellectual ability and experience to meet the serious challenges facing the church at this time.
"I hope that the new Pope continues the excellent work done by his predecessor, particularly in building bridges with other religions."
The Tánaiste and Progressive Democrats leader Mary Harney said today was "a historic day for the Catholic Church and its one billion followers."
"The death of Pope John Paul II had a profound impact on people throughout the world and it transcended many political and religious boundaries. He was universally respected as a great man of God, a bridge-builder and a peace-maker."
The Green Party leader Trevor Sergant also sent his best wishes to the new Pope.
"The human family and the wider web of life that is Creation yearn for the compassion which your predecessor, the late Pope John Paul II recognised when he made a plea for all to undergo an 'ecological conversion'," he said.
"May God strengthen and guide you in giving effect to the spiritual authority vested in you this day."
A Labour Party spokesman said his party wished the new Pope well.
SDLP leader Mark Durkan said Cardinal Ratzinger's many years of experience working closely with his predecessor will stand him in good stead.
"Pope John Paul II is truly a hard act to follow, but I am sure that Pope Benedict XVI will meet this great challenge in service to the church that he now leads. He will have the good wishes of many millions of people around the world in his work."