* Euro falls with Greece remaining a key focus
* Dollar and Swiss franc up vs most majors (Updates prices, adds quote, details, changes dateline, previous LONDON)
NEW YORK, June 27 (Reuters) - The euro fell against the dollar on Monday ahead of a key vote this week by the Greek parliament on austerity measures.
While the euro had been swinging between gains and losses it fell firmly into the red after Moody's said Greek banks have lost about 8 percent of their private-sector customer deposits so far this year. The ratings agency warned that those institutions would face severe cash shortage if outflows mount to 35 percent of their deposits. For more see [ID:nN1E75Q0CT].
Earlier the euro zone single currency had fallen to a record trough against the Swiss franc before the expected Thursday vote.
Analysts said the euro would be vulnerable to selling on any comments from Greek or other European officials which may cast doubt on the ballot's outcome, although many in the market believe the austerity measures will be approved.
Earlier the euro was boosted when French President Nicolas Sarkozy said French banks have agreed to roll over holdings of Greek debt for 30 years, President Nicolas Sarkozy said on Monday. [ID:nLDE75P0BM]
Moody's "adds to the uncertainty," said Kathy Lien, director of currency research at GFT Forex in New York.
"The fate of the euro/dollar hinges on the outcome of the vote."
In early New York trade, the euro EUR= was 0.1 percent lower at $1.4173, having spiked as high as $1.4236 and as low as $1.4101, according to Reuters data.
Demand from sovereign entities triggered the early move higher, which was exacerbated as stop-loss orders were tripped, traders said.
Technical analysts said the euro needed to close above its 100-day moving average, a key resistance level, to ensure a sustained rise higher.
Earlier the euro and the dollar fell to record lows against the Swiss franc on EBS EURCHF=EBS, after a dramatic rally in the safe-haven Swiss unit since April.
The possibility of a Greek default has raised concerns about the health of the European financial system and whether it can withstand such a credit event. Such worries triggered a sell-off in Italian banking shares late last week.
"Wednesday should see parliament agree to austerity measures endorsed by the EU and IMF, while Thursday's vote is likely to be contentious as it includes specific details related to privatisation, taxation and spending," said Eric Theoret, currency Strategist at Scotia Capital in Toronto.
"Sarkozy has provided euro-positive commentary relating to private sector involvement in a debt rollover with participation expected at 70 percent of current holdings."
Overall, the dollar has benefited from broad risk aversion stemming from the ongoing euro zone debt crisis, as investors have been cutting back on short positions in the U.S. currency. [IMM/FX]
Against the yen JPY=, the dollar rose 0.7 percent to 80.93 yen.
Analysts say persistent uncertainty about debt problems in Greece and the rest of the euro zone would support the dollar, but they warn that the struggling U.S. economy is far from stable, while Washington suffers from its own fiscal problem as it approaches its debt ceiling again which could haunt the dollar in the longer term.
"The fortunes of the USD will be determined largely by the mood in the euro zone as the USD is now fulfilling the role of 'not being the EUR', capitalizing on any bad news and retreating when the market gets more hopeful," Credit Agricole analysts said in a note.
"This has lent it more of a safe-haven status recently in relation to peripheral stories, but its reaction to softer U.S. data remains ambiguous." (Reporting by Nick Olivari; Additional reporting by Naomi Tajitsu in London; Editing by James Dalgleish)