The Archdiocese of Indianapolis has announced that it will no longer recognize a Jesuit high school as Catholic because it refuses to fire a teacher who is in a same-sex marriage.

A decree to be issued on Friday by Archbishop Charles Thompson says that Brebeuf Jesuit preparatory school “can no longer use the name Catholic and will no longer be identified or recognized as a Catholic institution”.

“Whether they teach religion or not, all ministers in their professional and private lives must convey and be supportive of Catholic Church teaching. The Archdiocese of Indianapolis recognizes all teachers, guidance counselors and administrators as ministers,” the archdiocese said in a statement on Thursday.

Archdiocesan-operated Indianapolis Roncalli high school has fired or suspended two guidance counselors in the past year because they are both in same-sex marriages.

However, Brebeuf is independent of the archdiocese despite being located in it and has “always maintained control of our school’s operations and governance, including our personnel decisions,” the school’s leaders said in an open letter on Thursday. The Indianapolis school has 793 students in grades nine to 12, with a faculty and staff of 132.

The Very Rev Brian Paulson, who heads the Midwest Province of Jesuits, said in a statement the archdiocese “requested verbally two years ago that Brebeuf Jesuit not renew this teacher’s contract because this teacher’s marital status does not conform to church doctrine”.

Paulson said the teacher does not teach religion and “is a longtime valued employee of the school”. He did not identify the teacher.

Brebeuf will appeal against the archdiocesan decision – to the Vatican if necessary, Paulson said.

“Brebeuf’s administration and board of trustees have determined that following the Archdiocese’s directive would not only violate their informed conscience on this particular matter, but also would set a concerning precedent for future interference in the school’s operations and other matters,” Paulson said.

Despite the decree, Brebeuf will continue to call itself an “independent Jesuit Catholic school”, its principal, Greg VanSlambrook, told the Associated Press.

“Independent Jesuit Catholic schools receive their governance and sponsorship from the Midwest Province” of Jesuits, VanSlambrook said. “We’d like to try to continue a partnership with the archdiocese.”

The Rev James Martin, a Jesuit priest who is one of the leading advocates for greater LGBT inclusion in the Catholic church, applauded the move by Brebeuf’s leadership.

“The targeting of LGBT employees in Catholic institutions must cease, and Brebeuf and the Jesuits are here standing with the marginalized,” Martin said in an email. “Despite what the Archdiocese says, this is the most Catholic thing that the school could do.”