* Dollar index close to 9-month low, euro/dlr sets 2-year high * Euro index at 2-year peak, could bother European policymakers * Weak U.S. jobs data cements view Fed stimulus to stay By Anooja Debnath LONDON, Oct 23 (Reuters) - The dollar struggled near a nine-month low on Wednesday after weak payrolls data prompted investors to all but rule out a cut in U.S monetary stimulus before next year. The dollar fell to as low as 79.137 against its basket of currencies, nearing this year's trough of 78.918 set in early February. It was last up 0.1 percent at 79.359. It touched a two-year low versus the euro, pushing the single currency to a two-year peak against its trade-weighted basket. The euro's steep ascent could cause concerns among European policymakers. The U.S. currency also extended losses against the yen - generally used as a safe haven by investors in times of political and economic uncertainty - as a drop in regional shares dented sentiment in Asia. Delayed data on Tuesday showed U.S. employers added far fewer workers than expected in September, suggesting the economy may have lost some momentum even before the 16-day government shutdown in Washington. "The weaker-than-expected payrolls report certainly supports investors' expectations that the Fed is likely to delay tapering quantitative easing into at least the first quarter of next year," said Lee Hardman, currency economist at BTMU. "In the very near term the dollar is likely to remain on the defensive even if the data begins to improve. Now that the shutdown has ended, it is going to take time to have greater clarity on the trajectory of the U.S. economy." A majority of U.S. primary dealers polled by Reuters now believe the Federal Reserve will not start cutting its $85 billion of monthly bond purchases until March. Strategists pointed to the Fed's Oct. 29-30 policy meeting, which could indicate whether there has been any substantial change to Fed policymakers' views on the economy. The dollar fell 0.9 percent against the yen to 97.32 yen , testing its 200-day moving average, now at about 97.27 yen, which was acting as near-term support. The yen rose broadly, with the euro falling 1.1 percent to 133.78 yen from Tuesday's four-year high of 135.52. EURO STRENGTH WORRIES Against the dollar, the euro had risen as high as $1.3793 on Tuesday, its highest level since November 2011. It was last down 0.2 percent at $1.3750. Strategists said if the euro's ascent gathered pace the European Central Bank could adopt some form of verbal intervention or other measures to dampen its strength. "Euro/dollar is trading at new highs for the year and the question is what will the response be from the ECB?" said Chris Turner, head of FX strategy at ING in a note to clients. "Euro zone headline inflation is low, and the ECB could repeat its February stance that the strong euro increases downside risks to inflation." He added that the ECB could hint at the need for more monetary stimulus via new Long-Term Refinancing Operations (LTRO) as it acknowledges that a "decline in excess liquidity could be pushing up money market rates. "Investors seem happy to play the weak dollar trend against the euro. $1.3710/30 looks a buy for a multi-day move to $1.3950/40."