Cardinal Christoph Schoenborn says the activists are "seeking a change of the (asylum) system at any price" even if they jeopardize the asylum-seekers' health.
About a dozen young men, mostly from Pakistan, are pressing for better living quarters, temporary work permits and other demands while waiting for a decision on their applications to remain in Austria.
Their supporters say several of them broke of a weeks-long hunger strike just recently.
Schoenborn's comments were reported Monday by the Kathpress news agency.
Like the cardinal, some politicians also have accused activists of encouraging a continuation of the protest for their own aims.