"The Church awaits them with open arms," Cardinal Darío Castrillón Hoyos, prefect of the Vatican Congregation for Clergy and of the Pontifical Commission "Ecclesia Dei," told the press when he summarized the conclusions of the Thursday meeting.
"We are on the way," he added. "We need the Lord's help, he is the one who guides everything."
"Now the best way is being studied," added the Colombian cardinal in response to the question about the possibility of a "prelature" under the Pope.
Archbishop Lefebvre, founder of the Society of St. Pius X, contested publicly some of the key elements of the Second Vatican Council.
Pope John Paul II stated in an 1988 the apostolic letter "Ecclesia Dei" that the "illegitimate" ordination of four bishops within the society by Archbishop Lefebvre was a "schismatic act."
That ordination truncated the attempt of an agreement between the Holy See and the group, which Cardinal Joseph Ratzinger -- then prefect of the Congregation for the Doctrine of the Faith -- had worked on in John Paul II's name.
Archbishop Lefebvre died in March 1991 and was succeeded by Bishop Bernard Fellay, one of the ordained prelates, in the leadership of the Society of St. Pius X. Benedict XVI received Bishop Fellay in private audience last Aug. 29.
"The meeting unfolded in an atmosphere of love of the Church and the desire to arrive at perfect communion," a Vatican communiqué reported afterward. "Aware of the difficulties, the willingness was expressed to advance gradually and in reasonable times."
According to several Italian newspapers today, some of the cardinals on Thursday requested that for reconciliation to take place, the followers of Archbishop Lefebvre must publicly accept Vatican II.
Cardinal Julián Herranz, president of the Pontifical Council for the Interpretation of Legislative Texts, told journalists that "the Pope listened to all with great interest and has made a perfect synthesis of the debate that took place."