* Euro headed for third monthly gain, up 1.1 pct in October
* Safe-haven demand falls as U.S. stocks rise after two-day closure
* Norwegian crown, Swiss franc gain versus euro
NEW YORK, Oct 31 (Reuters) - The euro rose against the dollar on Wednesday and was headed for its third straight month of gains as U.S. stocks rose after a two-day closure for Hurricane Sandy, denting safe-haven demand for the U.S. currency.
The yen, which also tends to rise in times of turmoil and fall when market sentiment improves, weakened across the board. The dollar is on track to post a gain of 2.5 percent against the yen in October, the best monthly performance since February.
On Wall Street, the Dow and S&P 500 rose at the open as equity markets reopened following a damaging storm in the U.S. Northeast that forced a two-day market closure, the first since 1888.
``Month-end and with most markets back to full liquidity it is likely to be a busy day as traders play catch up,'' said Camilla Sutton, chief currency strategist at Scotia bank in Toronto. ``Markets are adding risk to portfolios today.''
The euro rose 0.3 percent to $1.2988, having hit a session peak of $1.3021 and on track to post a gain of 1.1 percent this month.
The euro climbed 0.6 percent to 103.73 yen.
Traders said demand from Middle Eastern and Asian sovereign investors and a supranational also buoyed the euro.
``Today it is sentiment driving the euro up and stock markets are slightly positive, which has pushed it higher,'' said Antje Praefcke, currency strategist at Commerzbank in Frankfurt.
She added that trade was quiet before a holiday in many European countries on Thursday. Traders also said the euro's gains against the dollar may be limited due to expected month-end demand to buy dollars.
Insurance payouts in the wake of the storm could weigh on the dollar, although a rise in domestic demand for repair work could boost it.
Investors' focus began to shift to the U.S. jobs report for October. The Labor Department said it intended to release the October jobs data on Friday at 8:30 a.m. (1230 GMT), as scheduled, even though the storm forced the government to shut down for two days.
Employers are expected to have added 125,000 jobs to their payrolls in October, up from 114,000 in September, according to a Reuters survey of economists. The unemployment rate is forecast to tick up a tenth of a percentage point to 7.9 percent after a dramatic 0.3 percentage point fall in September.
Comments by Minneapolis Federal Reserve Bank President Narayana Kocherlakota, who strongly defended the U.S. central bank's ultra-easy monetary policy, weighed on the dollar.
``Over the next few months we think euro/dollar will break higher. We believe the market is underestimating the effect of the Fed's open-ended easing policy and tail risks will be priced out of the euro once Spain applies for a bailout.''
The issue of the U.S. economy's burgeoning fiscal cliff in the run-up to the presidential election on November 6 could add to the downside.
Some analysts said gains in the euro could be limited by uncertainty on when Spain may ask for a bailout and whether labor reforms in Greece will unlock its next aid tranche from international lenders.
The euro weakened 0.4 percent against the Norwegian crown to 7.3930 after Norway's oil fund said it held back from selling crowns in November after buying 500 million in October, stronger retail sales and better-than-expected credit figures.
Norway, one of Europe's strongest economies, kept interest rates steady at 1.5 percent on Wednesday and said it would slightly delay its next hike because damage from the euro zone crisis is still spreading.
Against the Swiss franc, the euro hit a three-week low of 1.20701 francs on trading platform EBS, with some market players citing increased repatriation flows from deleveraging by Swiss Bank UBS, which cut 10,000 jobs this week.
The dollar was up 0.3 percent at 79.86 yen, recovering from a fall to 79.25 yen on Tuesday, with improved risk appetite weighing on the safe-haven Japanese currency.