MILAN, June 5 (Reuters) - The market for risky perpetual bonds that banks count towards their capital will recover, the head of UniCredit said on Monday, adding that only at that time will his bank replace an issue it redeemed this month.

The market for Additional Tier 1 (AT1) bonds which lenders can use to beef up Tier 1 capital reserves has frozen following U.S. banking failures and the rescue of Credit Suisse, which wiped out holders of the bank's AT1 debt.

Nonetheless, "AT1s will survive and it's good that they survive," UniCredit CEO Andrea Orcel told a Bloomberg conference.

Though they are perpetual, AT1 bonds are normally repaid after five years as issuers exercise an option to redeem them. They need regulatory approval to do so, because this depletes their Tier 1 capital buffers.

Historically, banking supervisors demanded issuers refinanced the bond being called in order to grant approval for the repayment, but current market conditions make it too costly for lenders to issue new AT1 debt.

Some smaller lenders have stopped making use of call options in recent months, while UniCredit obtained supervisory approval to redeem a 1.25 billion euro AT1 bond in June. Reuters first reported in March it had sought clearance.

"We have a very high level of capital and of our total Tier1 (capital), less than 9% is AT1s," Orcel said.

"We're not 'hostage' to the product, we called back the 1.25 billion euro (AT1 bond) that we had in June and won't replace it until the market stabilises," he added.

Less than 7% of AT1 bonds currently on the market trade at prices that show investors have confidence the call will be exercised, Orcel said, showing that investors "feel banks cannot afford to replace them."

He expressed confidence this would only be a temporary phenomenon, but added that in the past investors had probably underestimated the risks these bonds carry. (Reporting by Valentina Za, editing by Gavin Jones)