By Richard Leong NEW YORK (Reuters) - Stock prices across major markets rose on Tuesday, led by U.S. technology and consumer sectors following the presidential debate between Hillary Clinton and Donald Trump, while oil prices fell on fading hopes of agreement on limiting production. A firmer dollar in the aftermath of the first Clinton-Trump debate helped send gold prices lower. Some investors deemed Democrat Clinton to have won the debate against Republican rival Trump. "From a market perspective, rightly or wrongly, there is an understanding that Mrs. Clinton would be a safe pair of hands, that there's very little uncertainty there," said Brad McMillan, chief investment officer for Commonwealth Financial in Waltham, Massachusetts. Anxiety about the future of Deutsche Bank curtailed Wall Street's advance and kept European equity markets little changed. U.S. and German government bond yields fell on safe-haven demand amid worries about Deutsche Bank and weaker oil prices. Investors have fretted over Germany's largest lender in the wake of a massive $14-billion demand from the U.S. Department of Justice to settle claims on bad mortgage-backed securities. U.S. consumer stocks were bolstered after a report showed consumer confidence rose to its strongest in nine years in September. The Dow Jones industrial average <.DJI> rose 133.47 points, or 0.74 percent, to 18,228.30, the S&P 500 <.SPX> gained 13.83 points, or 0.64 percent, to 2,159.93 and the Nasdaq Composite <.IXIC> added 48.22 points, or 0.92 percent, to 5,305.71. Overseas equity markets initially rose as betting markets suggested Democrat Clinton won the first debate over Republican Trump on Monday, supporting the view of no radical changes in U.S. policies on the domestic economy, international trade and foreign policy. Then Deutsche Bank shares dropped to another record low at 10.18 euros, leading to a reversal in European stocks that spread to selling in other regions. Deutsche shares recovered following remarks from a Justice Department official on the possibility of lower mortgage-related penalties for banks if they cooperate with authorities. Europe's broad FTSEurofirst 300 index <.FTEU3> eked out a 0.06 percent gain at 1,339.11. The MSCI world equity index <.MIWD00000PUS>, which tracks shares in 45 nations, rose 0.4 percent to 417.86. The U.S. 10-year Treasury note yield decreased 3 basis points to 1.558 percent, its lowest level in over two weeks, while the German two-year yield reached a near record low of -0.717 percent, according to Reuters data. CRUDE PRICES RETREAT Oil prices gave back most of Monday's gains on fizzling hopes of an agreement to freeze output as the world's largest producers gathered in Algeria to discuss ways to tackle a glut that has battered prices for two years. Brent crude ended down $1.38, or 2.91 percent, at $45.97 a barrel, while U.S. crude settled $1.26, or 2.74 percent, lower at $44.67 per barrel. It was too early to determine whether Monday's presidential debate will result in sizable changes among American voters for either Clinton or Trump in the Nov. 8th election, but the dollar, together with the Mexican peso and other higher-yielding currencies, enjoyed a bump. The dollar index <.DXY> was up 0.15 percent at 95.442, while the Mexican peso gained 2.3 percent at 19.435 peso per U.S. dollar. Mexico's currency had hovered near an all-time low at 19.735 pesos since last week on fears that a Trump presidency would threaten Mexico's exports to the United States, its single biggest market. Spot gold prices fell $10.50 or 0.79 percent, to $1,327.06 an ounce. (Additional reporting by Noel Randewich in San Francisco Yashaswini Swamynathan in Bengaluru; Marc Jones in London; Wayne Cole in Sydney; Editing by Nick Zieminski and Dan Grebler)