"These bank runs were triggered by text messages and were not related to underlying problems of the banking system, which is well capitalised and liquid. There has also been a loan from the European Union," Bas Bakker, the IMF mission chief to Austria, said at a news conference in Vienna.

Worries about the health of some Bulgarian banks have eased since runs on two major Bulgarian lenders this month, the Balkan state's central bank said on Monday, adding that the banking system was functioning normally.

Austrian National Bank Governor Ewald Nowotny took the same line and said Austrian banks - some of the biggest lenders in central and eastern Europe - were not affected.

"This is not a systemic problem of the Bulgarian banking system. It is a problem of specific banks and in fact what we see is deposits moving from these banks to Austrian-owned banks," he told the news conference.

UniCredit Bank Austria (>> UniCredit SpA) and Raiffeisen Bank International (>> Raiffeisen Bank International AG) are big players in Bulgaria.

Bakker was asked about separate moves by the government of Hungary to get banks to swallow more costs for foreign-exchange loans that went sour on borrowers when the forint currency depreciated.

He said the IMF had "taken note" of the proposals but played down the impact on Austrian banks.

"Of course this could increase losses made in Hungary and any country where profits go down or losses go up of course does not help the Austrian banks, but in the bigger picture it is not the most important country," he said.

Nowotny said the measures risked putting "quite strong burdens" again on Austrian and other lenders in Hungary.

"The Austrian banks and other banks have clearly been willing to cooperate in solving the problems involved with this but ... it is also clearly in the interest of the Hungarian economy to have banks that are well capitalised and that are able to provide for adequate loans," he said.

"It is in the enlightened self-interest of the Hungarian government to have a coordinated (approach) in this field."

Hungary's government moved on Friday to reduce bank charges on foreign currency mortgages, submitting legislation to parliament that could also help people with similar concerns about their forint loans.

Banks in Hungary include units of Belgium's KBC (>> KBC GROEP), Austria's Raiffeisen and Erste Group (>> Erste Group Bank AG), Italy's UniCredit and Intesa Sanpaolo (>> Intesa Sanpaolo SpA), and German-owned MKB Bank [BLGGM.UL].

(Reporting by Michael Shields; editing by John Stonestreet and Tom Pfeiffer)