By Tom Sims and Alexandra Schwarz-Goerlich

FRANKFURT/VIENNA (Reuters) -The European arm of Sberbank, Russia's biggest lender, faces failure, the European Central Bank warned on Monday, after savers demanded deposits, as the financial impact of Russia's invasion of Ukraine rippled through Europe.

The central bank said Sberbank subsidiary Sberbank Europe and two other subsidiaries were set to fail, after "significant deposit outflows" linked to "geopolitical tensions".

The ECB said the bank is likely to be unable to pay its debts, while Austria's Financial Market Authority imposed a moratorium on Sberbank Europe, which is based in the country.

Separately, Deutsche Boerse (DE:DB1Gn), the German stock exchange operator, said that it was suspending from trading a number of securities from Russian issuers with immediate effect. The list includes Sberbank and VTB Bank.

The moves underscore the impact of sanctions on Russia's banks, as well as the repercussions throughout Europe's financial system.

"We've triggered a run on this kind of bank," said Hans-Peter Burghof, a professor at the University of Hohenheim.

Banks and their lawyers are scrambling to assess the impact of a fresh wave of sanctions and the banishment of big Russian banks from the main global payments system SWIFT on their businesses.

British bank HSBC is beginning to wind down relations with a host of Russian banks including the second-largest, VTB, according to a memo seen by Reuters, as financial institutions start to implement restrictions on Russia.

Shares of leading banks sank with the European banking sector fell 5.5%, steeper than a 2.3% fall for the Euro Stoxx index.

The market turmoil came as Russian invasion forces seized two small cities in southeastern Ukraine and the area around a nuclear power plant, as Moscow's diplomatic and economic isolation deepened. Russia calls its actions in Ukraine a "special operation".

The banks with significant operations in Russia were hit the hardest. Austria's Raiffeisen Bank International fell 15% as it said it was working through the impact of sanctions.

Societe Generale (OTC:SCGLY) lost 10.7%, and UniCredit was 8% lower.

Germany's Deutsche Bank (DE:DBKGn), which opened a new Moscow headquarters in December, was down 8.5%. It said it would implement sanctions.

The ECB's warning extended to Sberbank subsidiaries in Croatia and Slovenia. Sberbank is majority owned by Russia.

The lender said in a statement that several of its subsidiaries saw "significant outflow of client deposits within a very short time" and that it was in close contact with regulators.

Sberbank's branches in Slovenia were closed until Wednesday and services temporarily limited to card transactions with a withdrawal limit of 400 euros a day, the Slovenian central bank said on Monday.

The Croatian central bank said depositors at Sberbank, which has about a 2% share of the country's banking market, would be allowed to withdraw just under 1000 euros a day.

Meanwhile, the Russian securities dropped by Deutsche Boerse also include Lukoil and Aeroflot.

Euroclear said is has closed its link to rival settlement house Clearstream Banking for settling trades in Russian securities in response to European Union financial sanctions.