Cyprus has cut salaries for state workers and a range of benefits -- steps international lenders have demanded in exchange for a bailout.
Archbishop Chrystostomos II said Friday that unions should "stay grounded and not take to the streets."
He said Cypriots will do what it takes to survive tough times ahead, even economizing on food, "but won't go hungry."
Several small protests were held outside parliament this week over austerity measures that Cyprus negotiated with the European Commission, the European Central Bank and the International Monetary Fund.
Cyprus is negotiating a bailout for its banks, which were heavily exposed to Greek debt.