* World stocks dip on uncertainty over U.S. tax reform
* British pound falls on concerns over leadership
* U.S. shares lackluster, European shares fall
* Oil steady amid Saudi tensions, rising U.S. production
* Graphic: World FX rates in 2017 http://tmsnrt.rs/2egbfVh (Updates to late afternoon, adds commentary)
NEW YORK, Nov 13 (Reuters) - World stock markets were down on Monday amid uncertainty over the fate of U.S. tax reform efforts, while Britain's pound fell on growing concerns about the future of Prime Minister Theresa May.
U.S. stock indexes made little ground. Some investors sought bargains after a few days of losses while others were put off by a dividend cut from heavyweight General Electric, as well as the company's plan to radically shrink to focus on sectors where it thinks it can make a profit.
Investors were waiting for any signs of compromise on U.S. tax policy after U.S. Senate Republicans on Thursday unveiled a plan that would cut corporate taxes a year later than a rival House of Representatives' bill.
"What the market seems to be focused on is if and when tax reform will be agreed on by Republicans in both the Senate and the House and how it'll fare in Congress," said Ryan Larson, head of U.S. equity trading at RBC Global Asset Management in Chicago.
The Dow Jones Industrial Average rose 35.76 points, or 0.15 percent, to 23,457.97, the S&P 500 gained 3.16 points, or 0.12 percent, to 2,585.46 and the Nasdaq Composite added 8.21 points, or 0.12 percent, to 6,759.15.
The pan-European FTSEurofirst 300 index lost 0.53 percent and MSCI's gauge of stocks across the globe shed 0.25 percent and was on track for a third straight day of declines after hitting an intraday record high on Thursday.
Sterling was down 6 percent against the dollar, on course for its biggest daily fall against the greenback since Nov. 2. It was also down 0.6 percent against the euro The Sunday Times newspaper reported that 40 members of parliament from May's Conservative Party agreed to sign a letter of no-confidence in her -- eight short of the number needed to trigger a party leadership contest.
"That just highlights some of the internal weakness that the Conservative party has within its own self and I think thats going to undermine the Brexit negotiations going forward," said Sireen Harajli, foreign exchange strategist at Mizuho in New York.
The dollar edged higher against a basket of other major currencies on Monday, recovering ground after logging a 0.6 percent decline last week. It rose 0.11 percent, with the euro up 0.03 percent to $1.1666.
U.S. Treasury two-year note yields hit a fresh nine-year high as the yield curve resumed its flattening, with investors pricing in a U.S. Federal Reserve interest rate hike in December. The two-year yield hit a nine-year peak of 1.679 percent, up from 1.662 percent last Friday.
Oil prices held steady in a tight range Monday after briefly testing lower, with support from Middle East tensions and record long bets by fund managers balanced by rising U.S. production.
A purge of Saudi Arabia's leadership by Crown Prince Mohammed bin Salman has raised concerns about political stability in the region's largest oil producer.
U.S. crude rose 0.09 percent to $56.79 per barrel and Brent was last at $63.18, down 0.54 percent on the day.
(Additional reporting by Saqib Iqbal Ahmed, Jessica Resnick-Ault, Gertrude Chavez-Dreyfuss in New York, Dhara Ranasinghe and Saikat Chatterjee in London, Hideyuki Sano in Tokyo; Editing by John Stonestreet and Chizu Nomiyama)