* Moody's cuts ratings of several Greek banks
* New ratings follow downgrade of nation's sovereign debt
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ATHENS, Dec 22 (Reuters) - Moody's cut the debt ratings of several Greek lenders on concerns about their profitability amid a slowing economy and the government's reduced ability to support them, after cutting Greece's sovereign debt earlier on Tuesday.
"We expect the earning power of Greek banks to be further weakened over the next few quarters as economic and business conditions remain unfavorable," Moody's said in a statement.
Moody's cut the deposit and debt ratings of the country's top lender, National Bank, to A1 from Aa3, and of EFG Eurobank, the second-biggest to A2 from A1.
Moody's downgraded Emporiki Bank, the Greek unit of France's Credit Agricole, to A2 from A1. It also cut its rating on the government-guaranteed debt rating of Alpha Bank, the third-biggest lender, to A2 from A1.
Greek banks are not burdened by toxic debt but are highly exposed to an economic slump across southeast Europe, where they operate.
"The action was prompted by a weakening of the banks' stand-alone financial strength, combined with Moody's reassessment of the country's ability to support its banking system," Moody's said.
Moody's cut Greece's debt to A2 from A1 on Tuesday over soaring deficits, becoming the third major rating agency to downgrade the highly-indebted country's rating this month. (Writing by Harry Papachristou; Editing by Andy Bruce)