Neuhaus died of complications from cancer, said Joseph Bottum, editor of First Things, a journal of religion and public policy that Neuhaus founded.
A one-time Lutheran minister, Neuhaus led a predominantly African American congregation in New York in the 1960s, advocating for civil rights and protesting the Vietnam War. With Rabbi Abraham Joshua Heschel and the Rev. Daniel Berrigan, a Catholic peace activist, Neuhaus led the antiwar group Clergy Concerned About Vietnam.
He later broke with the left, partly over the Supreme Court's 1973 ruling legalizing abortion. He converted to Catholicism in 1990, and a year later was ordained a priest.
He then worked to break down the historic mistrust between evangelicals and Catholics over their theological differences, helping build the coalition of churchgoers across faith traditions who became key to GOP electoral victories in recent years.
Neuhaus laid out his argument in the influential 1995 book "Evangelicals and Catholics Together: Toward a Common Mission," which he edited with Charles Colson, the Watergate figure turned born-again Christian. Neuhaus later was an informal advisor to Bush, who praised the priest for helping shape his own outlook on abortion.
Neuhaus also helped Bush define his policies on gay marriage and stem-cell research, among other issues. In 2005, Time magazine named the Catholic priest one of America's 25 most influential evangelicals.
"Father Neuhaus was an inspirational leader, admired theologian and accomplished author who devoted his life to the service of the Almighty and to the betterment of our world," Bush said in a statement. "He was also a dear friend, and I have treasured his wise counsel and guidance."
The Rev. James Martin, a Jesuit writer whose order Neuhaus frequently criticized, said Neuhaus was "an intelligent, impassioned and articulate defender of Catholic orthodoxy and arguably the leading conservative Catholic voice in this country."
A native of Canada, Neuhaus was born May 14, 1936, in Pembroke, Ontario, one of eight children of a Lutheran clergyman and his wife. He left home for the United States at 14 and worked odd jobs before enrolling at Concordia Theological Seminary in St. Louis, where he earned a divinity degree. At 25 he became pastor of St. John the Evangelist Church in Brooklyn.
Information about survivors was incomplete Thursday.