Pope Benedict XVI says he will follow his predecessor's tough line on abortion and euthanasia.
Large crowds turned out to see Pope Benedict XVI
He said that, like Pope John Paul II, he would remain "unequivocal" about the "inviolability of human life from conception to natural death".
The pontiff was outlining his vision of his papacy in a sermon at the ancient basilica of St John's in Lateran.
Meanwhile, a US priest has resigned as editor of a moderate Catholic magazine following pressure from the Vatican.
A pope "must constantly bind himself and the Church to the obedience of the word of God in the face of all the attempts to adapt it or water it down," Pope Benedict told a packed congregation.
"That's what Father John Paul II did when faced by all such attempts which were seemingly benevolent towards man.
"When faced with erroneous interpretations of freedom, he unequivocally underlined the inviolability of the human being, the inviolability of human life from conception to natural death.
"Freedom to kill is not a true freedom, but a tyranny that reduces the human being into slavery," he added, to applause from the congregation.
Large crowds greeted the Pope as he arrived at the cathedral to be installed as Bishop of Rome.
The ceremony was the last in Pope Benedict's formal assumption of the papacy since his election on 19 April.
Following his 30-minute homily, he drove to the nearby St Mary Major to pray in front of a statue of the Virgin Mary and lay flowers.
In a separate development, Father Tom Reese - a US Jesuit priest - has resigned after seven years as editor of the prominent American Catholic monthly, America.
His magazine had frequently commissioned articles critical of Rome on such controversial subjects as same-sex marriages, the paedophile priest scandal and whether Catholics who support abortion rights should be refused communion.
Father Reese announced his departure in a statement, but gave no reasons for going.
Jesuit sources in Rome say he had come under fire from the office of Cardinal Joseph Ratzinger, when he was in charge of Catholic doctrine and before his election to Pope.
Leading Jesuits rarely remain in the same job for more than seven years, says the BBC's David Willey in Rome.