Under church law, consecrating bishops without papal approval is considered a schismatic act and carries automatic excommunication for both the bishops being ordained and the bishop performing the ceremony.
"I urge you to consider carefully the spiritual good of the faithful, because the schismatic act you are about to undertake would deprive them of the licit, and in some cases, even valid reception of the sacraments," Leo wrote.
The dispute marks the first major challenge of Leo's pontificate. Since becoming pope, the American-born pontiff has emphasized healing divisions within the Church, including tensions with traditionalist Catholics who favor the old Latin Mass.
The Society of St. Pius X was founded after the Second Vatican Council, rejecting many of the church's reforms, including allowing Mass to be celebrated in local languages instead of Latin. The group has long argued that it is preserving authentic Catholic teaching.
The society defended its decision to consecrate four new bishops, saying there is a "state of necessity" requiring it to provide bishops for its faithful.
The planned ceremony echoes a similar confrontation in 1988, when the group's founder, Archbishop Marcel Lefebvre, consecrated four bishops without papal approval. The Vatican responded by excommunicating Lefebvre and the newly ordained bishops, though those excommunications were lifted in 2009 as part of an effort to restore relations.
Despite years of dialogue with the Vatican, the SSPX remains outside the church's formal structure.
The society has continued to expand in recent decades, reporting hundreds of priests, seminarians and religious members across dozens of countries, making it one of the largest traditionalist movements operating outside the Catholic Church's official authority.
The Associated Press contributed to this report.