Archbishop Carlo Maria Vigano wrote a letter to McCarrick that was published Monday on an Italian blog, Vigano's way of communicating after he went into hiding following his bombshell accusations against the pope in August.
In the letter, Vigano noted the Vatican is expected to shortly deliver its verdict against McCarrick after gathering testimony from at least three men who accused him of misconduct.
The McCarrick scandal has thrown the U.S. and Vatican hierarchy into crisis since it was apparently an open secret that the powerful retired archbishop of Washington slept with seminarians.
Vigano wrote that a public show of repentance would be a "gift" to the church to help it heal from the sex abuse crisis.
"Time is running out but you can confess and repent of your sins, crimes and sacrileges, and do so publicly," Vigano wrote. While saying McCarrick's own eternal salvation was at stake, Vigano also said the credibility of the church was also in the balance.
"A public repentance on your part would bring a significant measure of healing to a gravely wounded and suffering church," Vigano wrote. "Are you willing to offer her that gift?"
Vigano added fuel to the scandal when he demanded the pope himself resign over what he said was his role in the McCarrick cover-up. In an 11-page denunciation in August, Vigano said he told Francis of McCarrick's misdeeds in 2013 but that Francis went ahead and rehabilitated him from sanctions imposed by the previous pope.
Francis has never responded to Vigano's claims, but a top Vatican cardinal, Marc Ouellet, tried to shoot them down. Ouellet urged Vigano himself to repent, for having launched such an unprecedented attack against the pope.