Cardinal Gerhard Müller, the former prefect of the Congregation for the Doctrine of the Faith (CDF), has urged Pope Francis to “look for reconciliation” with his critic Archbishop Carlo Maria Viganò.

Speaking to EWTN’s The World Over programme, the German cardinal called on the Pope to “give answers to [his] accusations or questions”, saying: “The people of God have a right to know what happened.”

Archbishop Viganò, the former US nuncio, has accused Pope Francis of ignoring sanctions imposed on ex-cardinal Theodore McCarrick by Benedict XVI.

Cardinal Müller said that, while it is always possible for mistakes to be made, “we must learn from mistakes and we must become better in the prosecution of child and minor abuse”.

He said the Holy Father must work to preserve the unity of the Church and to overcome the divisions of the faithful.

“[The Pope] must be a symbol of the unity of the Church. We must overcome, with the help of the Holy Father, the splitting of the Church between conservatives and so-called liberals. We are one Church united in the faith and not of conservative or liberal ideology.”

Cardinal Müller said he had heard “nothing” about the sanctions apparently imposed on McCarrick by Benedict XVI. But he said a canonical process must be initiated against the former cardinal.

He also did not deny that Pope Francis blocked an investigation by the CDF into Cardinal Cormac Murphy-O’Connor.

The cardinal, who died last year, was accused of abusing a 13- or 14-year-old girl decades ago. Kent Police investigated the allegation but decided it could not be substantiated.

The claim was first passed on to the CDF in 2011 and the congregation decided there was not enough evidence to take it forward.

The case was reopened by the CDF in 2013 because of an “administrative gap” flagged up by the Archdiocese of Westminster, according to a report in the Tablet.

Asked if Pope Francis urged him to drop the case, Cardinal Müller said he was bound by pontifical secret, but that the CDF should be given more independence. Claims against bishops and cardinals require special approval from the Pope, he said.

“My proposal is to make the congregation in these cases more independent. It’s not good that the Pope takes over this right to stop a necessary investigation,” he said.

The cardinal also said that synods did not have magisterial authority.

In last month’s apostolic constitution Episcopalis Communio, Pope Francis said the synod’s final document would now form part of the “ordinary magisterium of the Successor of Peter,” subject to papal approval.

But Cardinal Müller said he did not know where the idea had come from that synods themselves could be magisterial.

“The Synod of the Bishops is not an ecumenical council – it does not have magisterial authority,” he said. “The Pope cannot change the basic constitution of the Church.”