(Adds details on the issue in paragraph 3 and 7-13, includes Bank of Cyprus in paragraph 5)

MADRID, June 13 (Reuters) - Spain's BBVA and Bank of Cyprus reopened the market with the issuance of the first euro-denominated contingent convertible bonds (CoCo) since the rescue of Credit Suisse in March, in what is seen as an attempt to restore confidence in the banks' riskiest debt instruments.

The Spanish bank said it aimed to raise between 750 million euros ($810.08 million) and 1 billion euros with this issuance.

According to a lead manager memo seen by Reuters, the issuance had already received orders worth over 3 billion euros.

The market for Additional Tier 1 (AT1) bonds, which lenders can use to beef up Tier 1 capital reserves, had been frozen following U.S. banking failures and the rescue of Credit Suisse, which wiped out its $17 billion AT1 bonds.

Separately, Bank of Cyprus also started selling on Tuesday a 220 million euros AT1, according to a lead manager memo also seen by Reuters. The debt -- which has attracted over 2.2 billion euros of orders from investors -- will pay a coupon of 11.875%, the memo added.

Meanwhile, BBVA said on Tuesday its AT1 bond had a redemption window of Dec. 21 2028. Its interest rate is guided in the 8.75% area.

The Spanish lender said the new issuance will provide flexibility to meet the redemption options of previous AT1 issues, the earliest of which is a 1 billion euro CoCo with a coupon of 5.875% that can be repaid on Sept. 24.

ING said in a note on Tuesday that BBVA's new issuance would make it "very likely" that the Spanish lender's 5.875% bond will be called in September.

The price of the 5.875% bond was up by over one cent on the euro on Tuesday.

BBVA declined to comment whether it will call the 1 billion euros CoCo in September.

ING also said that if the existing AT1 is not repaid in September, its coupon would be reset at +5.66% over the five-year swap rate, not far off the levels where the interest on the new bond is guided.

Banks usually sell these perpetual bonds - known as AT1 bonds - with five years before an option to repay is triggered.

BBVA's CoCo was underwritten by Barclays, BBVA, Bank of America, Citi, Goldman Sachs and Natixis, the lender said, in what would be the first perpetual bond issued by BBVA since July 2020.

Its issue was part of the group's financing plan for this year as this was its fifth debt issuance in 2023.

($1 = 0.9258 euros) (Reporting by Jesús Aguado, Chiara Elisei and Yoruk Bahceli; Editing by Louise Heavens and Ed Osmond)