Lima's Pontifical Catholic University of Peru will preserve its title as long as the institution "considers it relevant," said university director Marcial Rubio.
"Any decision on the matter is under the authority of the university's governing bodies," Rubio added.
The Holy See sought to withdraw the titles last weekend in a pontifical mandate and decree of the church's secretary of state, made on the basis of "canonical law."
Founded in 1917, the university was formally recognised by the church 25 years later.
The Vatican has accused PUCP of causing "serious damage to the interests of the church" since the 1960s, when a Peruvian priest and instructor at the university, Gustavo Gutierrez, founded the institution's guiding principle of "Liberation Theology," promoting social justice and pan-Latin American solidarity.
PUCP is an "institution created in Peru, governed by Peruvian law, not canonical law," Rubio said.
"This is the official name by which we are known domestically and internationally," he added.
"The university's assets are the property of the PUCP and are protected by the Peruvian constitution."
The Holy See said it has attempted to contact school directors several times since 1990 to no avail, attempting to make the establishment conform to the Vatican's interpretation of canonical law.
The university organised an assembly of staff, professors and students on Monday to discuss the Holy See's decision, which it calls "regrettable for all Catholics."
Some 22,000 students attend PUCP.