The scandal, which has shocked Austria's predominantly Catholic public, erupted after the Austrian weekly news magazine Profil published photographs showing leading clerics at a seminary fondling and kissing the male student priests.
The students were not children, and the pictures emerged after the start of a separate police investigation into alleged child pornography found on computers at the St Poelten seminary.
"We have separation of church and state in Austria, so I have no right to take a position as chancellor," Schuessel said in an interview on Austrian radio on Saturday.
"The authorities are investigating but, as a believer and Catholic, I want a quick and frank explanation."
On the child pornography investigation, a prosecutor is expected to announce next week whether formal charges will be filed on the basis of the police investigation.
Earlier this week, the head of an Austrian Catholic Church office for sex victims urged the bishop of St Poelten, Kurt Krenn, to resign immediately over the investigation.