* Debt worries boost safe-haven demand for Swiss franc
* Euro under pressure as Greek debt saga rolls onward
* S&P downgrades Greece, says default likely (Updates prices, adds quotes)
By Wanfeng Zhou
NEW YORK, June 13 (Reuters) - The euro fell to a record low against the Swiss franc on Monday, with more losses likely as disagreement among policymakers over how to solve Greece's debt crisis unsettled investors and boosted the safe-haven allure of the franc.
But the euro managed to gain versus the U.S. dollar, helped by central bank demand and after U.S. stock prices came off early lows. Concerns about a stalling U.S. economic recovery and a ballooning budget deficit also weighed on the dollar.
The single currency dropped as low as 1.2004 Swiss francs
European leaders are due to finalize a new rescue package for Greece at a Brussels summit on June 23-24. But deep divisions remain about how to get the private sector involved. Concerns are growing that Greece will eventually have to restructure its debt.
"If a compromise cannot be reached between these positions, there is a chance that the second rescue effort disintegrates, leaving Greece at the mercy of the bond markets," said Karl Schamotta, market strategist at Western Union Business Solutions, in Victoria, British Columbia.
"One suspects that policymakers will avoid such a dire outcome, but the uncertainty is weighing on investment decisions."
The euro last traded at 1.2068 francs, down 0.2 percent on the day. Earlier, it fell to a session low near 1.20 francs in thin liquidity after a break below 1.2050 triggered stop-loss orders and system-related selling.
"The Swiss franc is the currency to be in right now," said Greg Salvaggio, vice president of trading at Tempus Consulting in Washington. "The trend as investors need European exposure is to buy Swiss francs as opposed to the Scandies."
Price swings may have been exacerbated by low volume with many centers in Europe closed for a holiday.
Adding to the negative sentiment, Standard & Poor's cut Greece's long-term ratings by three notches to junk territory. The ratings agency said in a statement that a restructuring of Greece's debt -- either with a bond swap or by extending maturities on existing bonds -- looks increasingly likely. For details, see [ID:nN13126859]
The euro rose 0.5 percent to $1.4413
Resistance is seen at a concentration of former support levels around $1.4430/50, which includes previous intraday peaks in May and a 38.2 percent retracement of the May-to-June rise.
Investors also see a reduced likelihood of euro-zone rate hikes in the months ahead. Last week, the European Central Bank left inflation forecasts for 2012 unchanged, suggesting the pace of future interest-rate hikes may be slower than previously thought.
The rush toward safe-haven assets boosted the Swiss franc and kept the dollar pinned near record lows hit last week. The dollar was last down 0.7 percent at 0.8372 franc
The Swiss National Bank meets this week for a rate decision and is unlikely to signal any risk of intervention to cap the franc's strength.
The New Zealand dollar tumbled after a series of powerful earthquakes shook Christchurch, four months after the city was badly damaged by a 6.3 magnitude quake. The kiwi dropped 0.6 percent to trade at $0.8158