The Priestly Fraternity of St. Peter (FSSP), which celebrates the Traditional Latin Mass, addressed the situation in a July 16 statement.
"At this point, it is too early to tell what all the implications will be for the Priestly Fraternity of St. Peter, but we assure you that we remain committed to serving the faithful attending our apostolates in accordance with our Constitutions and charism as we have done since our founding," the order said in a statement provided to CNA.
"We must strive to see this Cross as a means of our sanctification, and to remember that God will never abandon His Church."
Other bishops have issued statements about the celebration of the Traditional Mass in their dioceses.
"I have informed our clergy that I am granting temporary permission for those priests competent in offering Mass in the Extraordinary Form to continue to do so in churches that already have an Extraordinary Form Mass on their schedule or in a private setting until further study and clarification can inform an appropriate implementation of this document," Archbishop Paul Coakley of Oklahoma City said in a July 16 tweet.
Archbishop Salvatore Cordileone of San Francisco told CNA July 16 that “The Mass is a miracle in any form: Christ comes to us in the flesh under the appearance of Bread and Wine. Unity under Christ is what matters. Therefore the Traditional Latin Mass will continue to be available here in the Archdiocese of San Francisco and provided in response to the legitimate needs and desires of the faithful.”
The Diocese of Arlington told CNA that all parishes that had planned on offering Masses in the Extraordinary Form would be able to do so.
“Bishop Burbidge has read the motu proprio regarding the 1962 Missal,” said a statement from Billy Atwell, chief communications officer for the Diocese of Arlington.
“He will review it in greater detail and offer further guidance to our priests in the near future. Parishes currently scheduled to offer Mass in the Extraordinary Form this weekend have received permission to do so.”
Bishop Daniel Flores of Brownsville, Texas said on Twitter that two parishes in his diocese that use the 1962 missal have "asked for & received permission to continue doing so while local norms appropriate to the motu proprio promulgated by His Holiness Pope Francis are being prepared."
Bishop Anthony Taylor of Little Rock, Arkansas said the new restrictions "do not apply" to two of the diocese' personal parishes, which are administered by the FSSP; however, the Traditional Latin Mass will cease to be celebrated in "regular parish churches" in the diocese.
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"There is no change for these [FSSP] parishes or the priests serving them. All that is required of them and the Fraternity of St. Peter (FSSP) priests serving them is that they accept the validity and legitimacy of the liturgical reform of Vatican II, which they do. 'Traditionis Custodes' does caution me not to establish any additional personal parishes for the celebration of the Latin Mass going forward," Bishop Taylor said in a July 16 letter.