BRAINTREE -- The Vatican's Congregation for Clergy has rejected appeals by former parishioners seeking to reverse the Archdiocese of Boston's decision to convert six church buildings to non-religious use, called "relegation for profane use" in Church parlance.

The decisions, dated March 20 to May 10, affect the buildings of St. Frances X. Cabrini in Scituate, Our Lady of Lourdes in Revere, St. Jeanne D'Arc in Lowell, Our Lady of Mount Carmel in East Boston, St. James the Great in Wellesley, and Mary Star of the Sea in Quincy. The ruling on St. Frances X. Cabrini in Scituate had previously been made public.

The churches were among those closed in 2004 as part of the archdiocese's parish reconfiguration. At the time, the archdiocese said the closures were required because of demographic changes, declining Mass attendance and a shortage of priests.

In making their appeals, the former parishioners had argued that the archdiocese did not show sufficiently "grave" reasons, as required by Church law, to relegate the six church buildings, clearing the way for their sale or conversion to other use.

Secretary of communication for the archdiocese Terry Donilon said the Vatican documents supporting the archdiocese's decision leave no room for confusion.

The reasons "are clear to the Vatican, they are clear to us, and they are clear to most people who read them. It is clear," he said.

Recently, the Vatican has reversed church relegation decisions in some other U.S. dioceses.

Donilon refuted suggestions from parish closure opponents that the decisions in Boston were influenced by Cardinal Seán P. O'Malley.

"We feel we did it right procedurally, we did it right on the substance, we provided an enormous amount of information with the Vatican to back up the decision that was made, and I think they are grasping at straws and I think they are trying to create a conspiracy theory that does not exist," he said.

In Wellesley and Scituate, former parishioners maintain vigils at their former churches.

He said those in vigil are not actively participating in their Catholic parish life, and invited those in vigil to return to "the fullness of parish life."

Donilon said archdiocesan calls to end vigils are not calls to end the appeals process.

"We are clearly going to respect the appeals process. We are going to allow it to play out. We have from day one, but I think it is fair to say, particularly in the case of the vigils, that they have to end," he said.

Under the appeals process the former parishioners can appeal to the Vatican high court, the Apostolic Signatura, Donilon said.

"Once the Signatura rules, they are speaking on behalf of the Holy Father. It is case closed at that point," he said.