Addressing the Christian group Faithworks, Blair said: "I don't want to end up with an American style politics with us all going out and beating our chests about our faith."
Faith was very important on a personal level, but it should not be part of the political process, he said.
His comments came after a week in which abortion became an electoral issue, with the cardinal of Britain's Roman Catholic Church backing the Conservative Party's stance on reducing the legal time limit for terminations.
The Archbishop of Canterbury Rowan Williams said he hopes parliamentary candidates would be questioned about their views on the issue.
Blair said he wanted church and faith groups to play a greater role in national life and paid tribute to their work for social justice at home and abroad.
Faith groups could work in partnership with government in inspiring a sense of community and mutual help, which was central to his vision of politics, he said.